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Direct Products of Groups  (Abstract Algebra)
 
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The direct product is a way to combine two groups into a new, larger group. Just as you can factor integers into prime numbers, you can break apart some groups into a direct product of simpler groups. If​ ​you​’d​ ​like​ ​to​ ​help​ ​us​ ​make​ ​videos more quickly,​ ​you​ ​can​ ​support​ ​us​ on ​Patreon​ at https://www.patreon.com/socratica We​ ​also​ ​welcome​ ​Bitcoin​ ​donations!​ ​​ ​Our​ ​Bitcoin​ ​address​ ​is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank​ ​you!! ************** We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition http://amzn.to/2oOBd5S Milne, Algebra Course Notes (available free online) http://www.jmilne.org/math/CourseNotes/index.html ************** Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W You​ ​can​ ​also​ ​follow​ ​Socratica​ ​on: -​ ​Twitter:​ ​@socratica -​ ​Instagram:​ ​@SocraticaStudios -​ ​Facebook:​ ​@SocraticaStudios ******** Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison
Views: 50705 Socratica
External Direct Product part 1
 
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Definition and theorems related to External Direct Product valuable for exam as well
Views: 1294 Reesha Education
Internal and External Direct Products Part 1
 
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In this video we discuss the definition of the internal and external direct products.
Views: 7345 Ben1994
Direct product | Group theory | Reducible representation
 
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In this lecture we will learn to calculate the combination of irreducible representation in direct product question from group theory chemistry. Important for csir net chemical science and Gate chemistry. Lecture by Csir net gate chemistry.
Product Groups Part 1
 
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In this video we discuss the construction of product groups.
Views: 3078 Ben1994
Direct Products of Groups
 
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We define the product of two groups and prove that the operation on the product does indeed define a group structure.
Views: 5798 Tim Hodges
Lec - 40 Cartesian Product of Groups or Direct Product of Groups
 
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This lecture contains External Direct Product and Internal Direct Product of Groups(Here Subgroup must be Normal and HK=G and H intersection K={e}). It also contains properties of the Cartesian product of groups and its applications. For Internal Direct Product please go through the lecture link given below https://www.youtube.com/watch?v=JR3b9FsZUx8&list=PL8WTUM4A_UNkZmDtNIxA_xU_lj4BqVtSn&index=56 #cartesianproductofgroups #directproductofgroups #grouptheory #abstractalgebra #csirnetmaths #iitjammsths
Views: 1012 Mathematical Science
Cyclic Groups  (Abstract Algebra)
 
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Cyclic groups are the building blocks of abelian groups. There are finite and infinite cyclic groups. In this video we will define cyclic groups, give a list of all cyclic groups, talk about the name “cyclic,” and see why they are so essential in abstract algebra. If​ ​you​’d​ ​like​ ​to​ ​help​ ​us​ ​make​ ​videos more quickly,​ ​you​ ​can​ ​support​ ​us​ on ​Patreon​ at https://www.patreon.com/socratica We​ ​also​ ​welcome​ ​Bitcoin​ ​donations!​ ​​ ​Our​ ​Bitcoin​ ​address​ ​is: 1EttYyGwJmpy9bLY2UcmEqMJuBfaZ1HdG9 Thank​ ​you!! ************** We recommend the following textbooks: Dummit & Foote, Abstract Algebra 3rd Edition http://amzn.to/2oOBd5S Milne, Algebra Course Notes (available free online) http://www.jmilne.org/math/CourseNotes/index.html ************** Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu9W You​ ​can​ ​also​ ​follow​ ​Socratica​ ​on: -​ ​Twitter:​ ​@socratica -​ ​Instagram:​ ​@SocraticaStudios -​ ​Facebook:​ ​@SocraticaStudios ******** Teaching​ ​Assistant:​ ​​ ​Liliana​ ​de​ ​Castro Written​ ​&​ ​Directed​ ​by​ ​Michael​ ​Harrison Produced​ ​by​ ​Kimberly​ ​Hatch​ ​Harrison
Views: 118649 Socratica
Group Theory 35, Internal Direct Products
 
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Group Theory 35, Internal Direct Products http://groupprops.subwiki.org/wiki/Internal_direct_product
Views: 3510 LadislauFernandes
GT6. Centralizers, Normalizers, and Direct Products
 
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Abstract Algebra: We consider further methods of constructing new groups from old. We consider centralizer and normalizer subgroups, which are useful when the group is non-abelian, and direct products. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-group-theory Master list at http://mathdoctorbob.org/UReddit.html
Views: 16139 MathDoctorBob
Direct Product of Normal Subgroups is Normal Proof
 
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Direct Product of Normal Subgroups is Normal Proof. In this video we prove that if A is a normal subgroup of G and B is a normal subgroup of H, then A x B is a normal subgroup of G x H.
Views: 1535 The Math Sorcerer
direct product of groups part 1 english
 
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There are three parts of this lecture. In all the three lectures following things has been explained: (i) External Direct Product of two groups. (ii) Internal Direct Product of two groups. (iii) External direct product of n copies of groups. (iv) Internal direct product of n copies of groups. (v) Internal direct product of countable many copies of groups. (vi) difference between direct product and direct sum of groups.
Views: 128 Vivek Kumar Jain
Direct product representation (CHE)
 
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Subject: Chemistry Paper: Applications of molecular symmetry and group theory Module: Direct product representation Content writer: Prof B S Garg
Views: 868 Vidya-mitra
Modern Algebra (Abstract Algebra) Made Easy-Part 7-Direct Products/Finitely Generated Abelian Groups
 
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http://www.pensieve.net/course/13 In this lecture, I define and explain in detail what Finitely Generated Abelian Groups are. I give examples, proofs, and some interesting tidbits that are hard to come by. Hope you like it! Works Cited: The only significant source for these videos is 'A First Course in Abstract Algebra', 2nd ed. by John Fraleigh. Though most of the problems and definitions come from this book, I explain the all the material & solutions in my own words.
Views: 29213 scalenescott
Lec - 41 Order of Elements in Cartesian Product of Groups
 
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Easy way to find the order of elements in direct product of groups #orderofelementsofcartesiangroup #orderofelemets #directproductofgroups #cartesianproductofgroups #grouptheory #abstractalgebra
Views: 1214 Mathematical Science
301.8G Extra: External Direct Product & Short Exact Sequence
 
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The external direct product of A and C is always a solution to the "product problem" of short exact sequences. Here we see how.
Views: 33 Matthew Salomone
Direct product of groups
 
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Direct product of groups In group theory, the direct product is an operation that takes two groups G and H and constructs a new group, usually denoted G × H.This operation is the group-theoretic analogue of the Cartesian product of sets and is one of several important notions of direct product in mathematics. =======Image-Copyright-Info======== License: Creative Commons Attribution-Share Alike 3.0 (CC BY-SA 3.0) LicenseLink: http://creativecommons.org/licenses/by-sa/3.0 Author-Info: derivative work: Pbroks13 (talk) Cyclic_group.png: Jakob.scholbach Image Source: https://en.wikipedia.org/wiki/File:Cyclic_group.svg =======Image-Copyright-Info======== -Video is targeted to blind users Attribution: Article text available under CC-BY-SA image source in video https://www.youtube.com/watch?v=szHP0cnyq-o
Views: 359 WikiAudio
Direct Product of Rings
 
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We define the direct product of two rings.
Views: 316 Ranthony Clark
301.8B Defining, Motivating, and Modeling Direct Products
 
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The direct product of two groups G and H is a group in which the elements and algebra of both G and H coexist side-by-side in an ordered pair. We look at two models for the direct product of cyclic groups, trying to tell the difference between two examples of order 12.
Views: 68 Matthew Salomone
direct product of groups part 3
 
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This is the third and last lecture in the series of lectures Direct Product of Groups. In this lecture direct product of n copies of groups is explained and the difference between direct product and direct sum is explained.
Views: 135 Vivek Kumar Jain
Direct product representation
 
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Subject: Chemistry Paper: Applications of Molecular Symmetry and Group theory Module: Direct product representation Content Writer:
Views: 930 Vidya-mitra
Group Theory 32, External Direct Products
 
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Group Theory 32, External Direct Products
Views: 7026 LadislauFernandes
Visual Group Theory, Lecture 3.4: Direct products
 
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Visual Group Theory, Lecture 3.4: Direct products There is a natural way to put a group structure on the Cartesian product of two groups. In this lecture, we introduce this concept algebraically, and show several different ways to visualize this, using tools such as Cayley diagrams and multiplication tables. We also look at subgroups and normal subgroups of direct products, and establish a few basic properties. Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html
Views: 5262 Professor Macauley
Direct Products of Finite Cyclic Groups Video 1
 
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Direct Products of Finite Cyclic Groups Video 1. How to determine if a direct product of finite cyclic groups is itself cyclic. This video has very easy examples.
Views: 3174 The Math Sorcerer
first lecture internal direct product by sir kamil nawaz
 
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INTERNAL DIRECT PRODCUT FIRST LECTURE BY SIR KAMIL NAWAZ GROUP THEORY ADVANCE ALGEBRA MSC MATHEMATICS DEFINITION OF INTERNAL DIRECT PRODDUCT
Views: 2123 kamil nawaz
Quantum Chemistry 12.15 - Irrep Direct Products
 
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Short lecture on irrep direct products. The irreducible representations of a point group form a group themeselves through their multiplication. This is relevant in molecular term symbols, where the direct product of all molecular orbital irrep labels results in the irrep of the total wavefunction, for example singlet A1 as the ground state of H2O. Symmetry at Otterbein: http://symmetry.otterbein.edu Character Tables: http://symmetry.jacobs-university.de/ Notes Slide: http://i.imgur.com/IxfRDlf.png --- About TMP Chem --- All TMP Chem content is free for everyone, everywhere, and created independently by Trent Parker. Email: [email protected] --- Video Links --- Chapter Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicKX9g2IA7FAe0pihiwJCjLG Course Playlist: https://www.youtube.com/playlist?list=PLm8ZSArAXicL3jKr_0nHHs5TwfhdkMFhh Course Review: https://www.youtube.com/playlist?list=PLm8ZSArAXicLTRn3cJyyU1TiU7n_Pp4X1 Other Courses: https://www.youtube.com/playlist?list=PLm8ZSArAXicIXArfap9Tcb8izqRPvE0BK Channel Info: https://www.youtube.com/playlist?list=PLm8ZSArAXicLlGO4Rvpz-D6vX8MFbOn4V --- Social Links --- Facebook: https://www.facebook.com/tmpchem Twitter: https://www.twitter.com/tmpchem LinkedIn: https://www.linkedin.com/in/tmpchem Imgur: https://tmpchem.imgur.com GitHub: https://www.github.com/tmpchem --- Equipment --- Microphone: Blue Yeti USB Microphone Drawing Tablet: Wacom Intuos Pen and Touch Small Drawing Program: Autodesk Sketchbook Express Screen Capture: Corel Visual Studio Pro X8
Views: 3982 TMP Chem
Direct Products of Finite Cyclic Groups Video 2
 
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Direct Products of Finite Cyclic Groups Video 2. How to determine if the direct product of finite cyclic groups is cyclic. Better examples than the first video.
Views: 2022 The Math Sorcerer
Lec - 15 Application of Sylow's Theorem || Internal Direct Product || Part V
 
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Application of Sylow's Theorem with Internal Direct Product Why group of order 15, 35, 65, 91 are cyclic? Why group of order 1001 is Abelian? #applicationofsylow #sylowtheoremwithidp #internaldirectproduct #sylowpackage #grouptheory #abstractalgebra
301.7G Extra: Counting an Internal Direct Product
 
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When we multiply the elements of two subgroups of G together, how many elements are there in the resulting set? This product formula theorem is a valuable element in classifying groups whose order is twice a prime, and is also an illustration of a more general product construction that we'll use to understand how larger groups are put together from smaller.
Views: 54 Matthew Salomone
Abstract Algebra, Lec 18A, External Direct Products Calculations & Isomorphisms, Normal Subgroups
 
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(0:00) Lecture plan. (0:28) Criterion for when the external direct product of cyclic groups is cyclic and Example (Z4 + Z9 is isomorphic to Z36). (6:40) Extension to the external direct product of more than two cyclic groups (Example: Z2 + Z3 + Z25 is isomorphic to Z150). (7:27) When the factors have orders that are not relatively prime, the resulting group will not be cyclic (Example: Z4 + Z6 is not cyclic). (8:40) Example: Find the number of elements of various orders in Z8 + Z8. (12:23) Isomorphism facts about U-groups (group of units modulo n); Examples: U(385) is isomorphic to Z4 + Z6 + Z10 and U(225) is isomorphic to Z6 + Z20. (19:39) Facts about subgroups of U-groups. (20:11) Definition of a normal subgroup of a group (in terms of left and right coset equality). (21:30) Basic facts and examples. (24:12) Subgroups of index 2 in a group are normal in that group. (26:28) Transitivity might not be satisfied. (27:40) Normal subgroup test. (29:20) For any subgroup H of G and any x in G, the set xHx^(-1) is a subgroup of G. (30:33) Proof of this last fact using the two-step subgroup test.
Views: 410 Bill Kinney
Group Theory :Product of Subgroup and It is not necessity product is again subgroup
 
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Topic Covered : Product of Subgroup and Theorem and its examples. Multiplication of Subgroup Facebook page .. https://www.facebook.com/Math.MentorJi/ Graduate Math app :https://goo.gl/vo2Tj2 thoerem related subgroup : https://youtu.be/cfT3ZFmfNLI Subgroup and examples = https://youtu.be/H7CKR1Nevnw (a+b)^2 =https://youtu.be/5i5yL2BCwpc permuatation group theory :https://youtu.be/-VvUsxsujyc Examples of singularity : https://youtu.be/cgsB8Z5WSPk Riemann Sum : https://youtu.be/Z3Ecy2Zwukw Riemann Sum problems https://youtu.be/LKuZreMPiRQ infimum and supremum https://youtu.be/mK6NZznoZeg Dirichlet and able test https://youtu.be/WyoMpdh7f0c uniform convergence : https://youtu.be/_WWsMl0_9BI MN Test of uniform : https://youtu.be/r5yec-FtlUE pointwise convergence:http://youtu.be/o_0YjNo_v64 Cauchy integral Formula :http://youtu.be/LEJBT0nLngM complex integration : http://youtu.be/s2wPryo_Hfs Limit pt .of infimum & supremue :http://youtu.be/zIn8CTcX-6A comparsion test(convergence) : http://youtu.be/02IncEDug2Y Cauchy all theorm :http://youtu.be/G5ZTzjN8KQA Cauchy sequence with example :http://youtu.be/B-7cUVXSZeI Cauchy nth root test :http://youtu.be/AOPIZsR4JkU Basics Of Sequence And Series :http://youtu.be/IZgNfFc481M Convergence sequence : http://youtu.be/c3Il3eEPvF0 Power series radius,domain convergent:https://youtu.be/C8Bw-gFC1Gg
Views: 2156 Math Mentor
Internal and External Direct Products Part 2
 
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In this video we discuss the definition of the internal and external direct products.
Views: 2445 Ben1994
Abstract Algebra 8.3: Direct Products of Cyclic Groups
 
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We look at an easy way to determine whether the direct product of cyclic groups is itself cyclic or not.
Views: 12 Patrick Jones
Abstract Algebra 8.1: External Direct Product
 
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We define the external direct product of a finite number of groups, do some examples, and show why up to isomorphism there are only two groups of order 4.
Views: 32 Patrick Jones
Group Theory 33, Properties of External Direct products
 
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Group Theory 33, Properties of External Direct products
Views: 5408 LadislauFernandes
Abstract Alg, Lec 21A, Internal Direct Products, Homomorphisms, Kernels, First Isomorphism Thm
 
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(0:00) Lecture plan. (0:29) Exam 2 next class period. (1:35) Internal direct product of two normal subgroups and the proof that it is isomorphic to the corresponding external direct product. (18:42) Definition of a group homomorphism and the kernel of a group homomorphism (with comments linear transformations and null spaces and about preimage (inverse image) notation). (22:15) Kernels are normal subgroups and cosets of the kernel are preimages of individual elements in the image ("range"), and a verification. (29:19) First Isomorphism Theorem and the idea of its proof. (35:51) Normal subgroups are kernels.
Views: 155 Bill Kinney

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