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  • IA-automorphism-balanced subgroup
    ==Definition== A subgroup of a group is termed an IA-automorphism-balanced subgroup or IA-balanced subgroup if every IA-automorphism of the whole ... ...
    1 KB (112 words) - 21:12, 19 January 2013
  • IA-automorphism-invariant subgroup
    ==Definition== A subgroup of a group is termed an IA-automorphism-invariant subgroup if it is invariant under all IA-automorphisms of the whole group. ... ...
    1 KB (130 words) - 13:26, 30 June 2009
  • IA-automorphism group of finite p-group is p-group
    ==Statement== Suppose p is a prime number and G is a finite p-group. Then, the group of IA-automorphisms of G is also a finite p-group (for the ... ...
    815 bytes (123 words) - 06:39, 25 November 2012
  • IA-automorphism group of finite nilpotent group has precisely the same prime factors of order as the derived subgroup
    ==Statement== Suppose G is a finite nilpotent group. Then, the IA-automorphism group of G (i.e., the subgroup of the automorphism group of G comprising ... ...
    2 KB (363 words) - 06:38, 25 November 2012
  • IA-balanced subgroup
    #REDIRECT IA-automorphism-balanced subgroup ... ...
    47 bytes (3 words) - 19:21, 19 January 2013
  • Semicomplete group
    #redirect group in which every IA-automorphism is inner ... ...
    59 bytes (8 words) - 01:07, 22 November 2012
  • IA-automorphism
    ==History== The term IA-automorphism was coined by Seymour Bachmuth in his paper Automorphisms of free metabelian groups. ==Definition== ... ...
    3 KB (335 words) - 22:13, 19 May 2015
  • IA not implies class-preserving
    ==Statement== ===Property-theoretic statement=== The automorphism property of being an IA-automorphism does not imply the automorphism property ... ...
    2 KB (245 words) - 05:44, 19 May 2015
  • Subgroup with canonical abelianization
    ==Definition== A subgroup with canonical Abelianization is a subgroup satisfying the following property: any defining ingredient::inner automorphism ... ...
    602 bytes (66 words) - 21:46, 26 July 2009
  • Characteristic direct factor
    ==Definition== A subgroup of a group is termed a characteristic direct factor if it is a characteristic subgroup as well as a direct factor. ... ...
    4 KB (455 words) - 02:59, 20 January 2013
  • Group in which every IA-automorphism is inner
    ==Definition== A group in which every IA-automorphism is inner, sometimes also called a semicomplete group, is defined as a group in which every ... ...
    895 bytes (100 words) - 01:06, 22 November 2012
  • Locally inner automorphism
    ==Definition== inner on finite tuples, inner on finitely generated subgroups ===Definition with symbols=== An automorphism \sigma of a group G ... ...
    2 KB (234 words) - 01:35, 8 January 2010
  • IA-automorphism group of nilpotent group equals stability group of lower central series
    ==Statement== ===For an individual automorphism=== Suppose G is a nilpotent group. Then, the following are equivalent for an automorphism \sigma of G: ... ...
    3 KB (546 words) - 06:25, 25 November 2012
  • Preserves conjugacy classes for a generating set implies IA
    ==Statement== Suppose G is a group, S is a generating set for G, and \sigma is an automorphism of G such that \sigma(x) is in the conjugacy class ... ...
    2 KB (263 words) - 19:00, 19 May 2015
  • Perfect characteristic subgroup
    ==Definition== A subgroup of a group is termed a perfect characteristic subgroup if it satisfies the following equivalent conditions: ... ...
    723 bytes (88 words) - 13:32, 30 June 2009
  • Automorphism that preserves conjugacy classes for a generating set
    ==Definition== Suppose G is a group and \sigma is an automorphism of G.We say that \sigma is an automorphism that preserves conjugacy classes ... ...
    3 KB (458 words) - 07:59, 19 May 2015
  • Class-preserving automorphism
    ==Definition== An defining ingredient::automorphism of a group is termed a class-preserving automorphism or class automorphism if it takes each ... ...
    5 KB (562 words) - 14:42, 1 September 2023
  • Endomorphism structure of M16
    This article is about the structure of endomorphisms of M16 (GAP ID: (16,6)) which we will take as having the following presentation: ... ...
    12 KB (2,022 words) - 15:12, 13 June 2011
  • Endomorphism structure of quaternion group
    This article discusses the endomorphism structure of the quaternion group, a group of order 8 given by the following multiplication table: ... ...
    7 KB (1,106 words) - 14:15, 26 August 2024
  • Characteristic implies normal
    To learn more about the similarities and differences between characteristicity and normality, refer the survey article Characteristic versus normal ... ...
    9 KB (1,259 words) - 22:29, 16 September 2011
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