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20A05 - Group theory and generalizations :: Foundations :: Axiomatics and elementary properties

  1. C_{mn}\cong C_m\times C_n when m, n are relatively prime owned by yesitis
  2. a characterization of groups owned by yark
  3. a group of even order contains an element of order 2 owned by azdbacks4234
  4. a subgroup of index 2 is normal owned by alozano
  5. alternative definition of group owned by pahio
  6. automorphism group of a cyclic group owned by rm50
  7. center of a group owned by yark
  8. characteristic subgroup owned by yark
  9. class function owned by djao
  10. conjugacy class owned by djao
  11. conjugate stabilizer subgroups owned by Thomas Heye
  12. core of a subgroup owned by yark
  13. coset owned by djao
  14. cyclic group owned by yark
  15. derived subgroup owned by yark
  16. division in group owned by pahio
  17. double coset owned by yark
  18. equivariant owned by bwebste
  19. Euler-Fermat theorem owned by Wkbj79
  20. example of straight-line program owned by Algeboy
  21. examples of finite simple groups owned by mathcam
  22. examples of groups owned by AxelBoldt
  23. Feit-Thompson conjecture owned by PrimeFan
  24. Feit-Thompson theorem owned by mathcam
  25. finite subgroup owned by pahio
  26. finitely generated group owned by yark
  27. first isomorphism theorem owned by rspuzio
  28. fourth isomorphism theorem owned by bwebste
  29. fundamental homomorphism theorem owned by yark
  30. generating set of a group owned by yark
  31. generator owned by Wkbj79
  32. group owned by drini
  33. group actions and homomorphisms owned by CWoo
  34. group homomorphism owned by yark
  35. groups in field owned by pahio
  36. groups of small order owned by Daume
  37. groups with abelian inner automorphism group owned by rm50
  38. homogeneous group owned by whm22
  39. homogeneous space owned by rmilson
  40. homomorphic image of group owned by pahio
  41. ideal of elements with finite order owned by pahio
  42. identity element owned by mclase
  43. injection can be extended to isomorphism owned by pahio
  44. inner automorphism owned by rmilson
  45. inverse of a product owned by pahio
  46. inverse of inverse in a group owned by cvalente
  47. isomorphic groups owned by alozano
  48. isomorphism owned by djao
  49. kernel owned by rmilson
  50. left and right cosets in a double coset owned by asteroid
  51. method of repeated squaring owned by Algeboy
  52. more on division in groups owned by CWoo
  53. non-isomorphic groups of given order owned by pahio
  54. nonabelian group owned by drini
  55. normal closure owned by yark
  56. normal is not transitive owned by Wkbj79
  57. normal subgroup owned by djao
  58. normality of subgroups is not transitive owned by yark
  59. normality of subgroups of prime index owned by azdbacks4234
  60. normalizer owned by yark
  61. one-sided normality of subsemigroup owned by lars_h
  62. order (of a group) owned by mathcam
  63. order of elements in finite groups owned by rm50
  64. order of products owned by pahio
  65. presentation of a group owned by rmilson
  66. proof of first isomorphism theorem owned by uriw
  67. proof of fourth isomorphism theorem owned by aoh45
  68. proof of second isomorphism theorem for groups owned by yark
  69. proof of third isomorphism theorem owned by Thomas Heye
  70. proof that all cyclic groups are abelian owned by Wkbj79
  71. proof that all cyclic groups of the same order are isomorphic to each other owned by Wkbj79
  72. proof that all subgroups of a cyclic group are cyclic owned by Wkbj79
  73. proof that group homomorphisms preserve identity owned by odenskrigare
  74. proof that group homomorphisms preserve inverse owned by odenskrigare
  75. Proof: The orbit of any element of a group is a subgroup owned by drini
  76. properties of conjugacy owned by pahio
  77. regular group action owned by mathcam
  78. second isomorphism theorem owned by djao
  79. solvable group owned by djao
  80. straight-line program owned by Algeboy
  81. structure of (\mathbb{Z}/n\mathbb{Z})^{\times} as an abelian group owned by rm50
  82. subgroup owned by Daume
  83. subgroups of finite cyclic group owned by pahio
  84. the derived subgroup is normal owned by juanman
  85. the kernel of a group homomorphism is a normal subgroup owned by alozano
  86. third isomorphism theorem owned by yark
  87. types of homomorphisms owned by rspuzio
  88. uniqueness of inverse (for groups) owned by waj
  89. word owned by juanman

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