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Flashcards

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Liam McGahan Group Theory 2 English 21 cards

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Cards in this deck (21)

  1. 1Binary Operations What are they? When are they associative? What is an Identity element for them? When are the Invertible?Binary Operations What are they? When are they associative? What is an Identity element for them? When are the Invertible?
  2. 2What are 3 important properties any associative operation on a set which contains an identity elementWhat are 3 important properties any associative operation on a set which contains an identity element
  3. 3How is a group defined? What makes a group abelian?How is a group defined? What makes a group abelian?
  4. 4Prove the following?Prove the following?Prove the following?
  5. 5Prove the theoremProve the theoremProve the theorem
  6. 6Define Modular Arithmetic and Modular MultiplicationDefine Modular Arithmetic and Modular Multiplication
  7. 7Prove the following?Prove the following?Prove the following?
  8. 8What is the Symmetric Group?What is the Symmetric Group?
  9. 9What is a Permutation?What is a Permutation?
  10. 10Define the support and when are two permutations disjoint?Define the support and when are two permutations disjoint?
  11. 11Define the orbitDefine the orbit
  12. 12Prove The followingProve The followingProve The following
  13. 13Prove the followingProve the followingProve the following
  14. 14What is the commutator of 2 elements of a group and what properties does it have?What is the commutator of 2 elements of a group and what properties does it have?
  15. 15What makes an element of a group the conjugate of another element of said group?What makes an element of a group the conjugate of another element of said group?
  16. 16Prove the following?Prove the following?Prove the following?
  17. 17Define a conjugacy classDefine a conjugacy class
  18. 18Prove the followingProve the followingProve the following
  19. 19When does an element of a group have finite order or infinite order?When does an element of a group have finite order or infinite order?
  20. 20Prove the FollowingProve the FollowingProve the Following
  21. 21—

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2 Group Theory Flashcards on Untitled, created by Liam McGahan on 20/01/2025.
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Liam McGahan
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