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Flashcards

Abstract Algebra Review

Alyssa Baxter English 51 cards

Group definition

Cards in this deck (51)

  1. 1Group definitionGroup definition
  2. 2Identity and Inverse Chapter 2 TheoremIdentity and Inverse Chapter 2 Theorem
  3. 3Cancellation and souls-shoes (ch 2)Cancellation and souls-shoes (ch 2)
  4. 4Subgroup DefinitionSubgroup Definition
  5. 5One-step subgroup testOne-step subgroup test
  6. 6Two-step subgroup testTwo-step subgroup test
  7. 7(the subgroup generated by a) is a _______ of Gsubgroup
  8. 8Center of a group def & theoremCenter of a group def & theorem
  9. 9Centralizer def & theoremCentralizer def & theorem
  10. 10cycliccyclic
  11. 11i=j theoremi=j theorem
  12. 12Fundamental Theorem of cyclic groupsFundamental Theorem of cyclic groups
  13. 13Permutation and Permutation GroupPermutation and Permutation Group
  14. 14Theorem: Disjoint cycles ________commute
  15. 15The order of a permutation is the...LCM of the lengths of its disjoint cycles
  16. 16Every element of S_n can be written asa product of transpositions (2 cycles)
  17. 17even permutationseven permutations
  18. 18alternating group (A_n)alternating group (A_n)
  19. 19isomorphismisomorphism
  20. 20Cayley's TheoremCayley's Theorem
  21. 21AutomorphismAutomorphism
  22. 22Thm: Aut(G) and Inn(G) are...Thm: Aut(G) and Inn(G) are...
  23. 23Thm: Aut(Z_n) is isomorphic toU(n)
  24. 24CosetsCosets
  25. 25LaGrange TheoremLaGrange Theorem
  26. 26Any group of prime order is...cyclic
  27. 27In a finite group, the order of each element....divides the order of the group
  28. 28orbit and stabilizerorbit and stabilizer
  29. 29orbit-stab thmorbit-stab thm
  30. 30external direct productexternal direct product
  31. 31external direct product theoremexternal direct product theorem
  32. 32normal subgroupnormal subgroup
  33. 33normal subgroup testnormal subgroup test
  34. 34Thm: If H is a normal subgroup of G then the set G/H =Thm: If H is a normal subgroup of G then the set G/H =
  35. 35G/Z theoremG/Z theorem
  36. 36internal direct productinternal direct product
  37. 37If G is a group of order p^2, then either...If G is a group of order p^2, then either...
  38. 38homomorphismhomomorphism
  39. 39kernelkernel
  40. 40—
  41. 41Fundamental Thm of Group HomosFundamental Thm of Group Homos
  42. 42determining isomorphism classesdetermining isomorphism classes
  43. 43ring defring def
  44. 44things about ringsthings about rings
  45. 45subring defsubring def
  46. 46subring test thmsubring test thm
  47. 47zero-divisorzero-divisor
  48. 48integral domain defintegral domain def
  49. 49Euclid's LemmaEuclid's Lemma
  50. 50integral domain is a commutative ring...integral domain is a commutative ring...
  51. 51fieldfield

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Flashcards on Abstract Algebra Review, created by Alyssa Baxter on 05/12/2022.
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Alyssa Baxter
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