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• 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
• Group in which every class-preserving automorphism is inner
  ==Definition== A group in which every class-preserving automorphism is inner is a group with the property that any defining ingredient::class ... ...
  1,006 bytes (121 words) - 19:44, 1 October 2008
• Extended class-preserving automorphism
  ==Definition== An automorphism \sigma of a group G is termed an extended class-preserving automorphism if it sends every element either to an ... ...
  649 bytes (76 words) - 23:49, 1 September 2009
• Rational class-preserving automorphism
  ==Definition== An automorphism \sigma of a group G is termed a rational class-preserving automorphism if it satisfies the following equivalent ... ...
  936 bytes (112 words) - 00:00, 4 September 2009
• Class-preserving automorphism-invariant subgroup
  #redirect normal subgroup ... ...
  29 bytes (3 words) - 18:56, 19 January 2013
• Cyclic quotient of automorphism group by class-preserving automorphism group implies same orbit sizes of conjugacy classes and irreducible representations under automorphism group
  ==Statement== Suppose G is a finite group and K is a fact about::splitting field for G. Suppose the quotient group of the automorphism group ... ...
  2 KB (317 words) - 17:09, 3 May 2015
• Finite group with cyclic quotient of automorphism group by class-preserving automorphism group
  ==Definition== A finite group with cyclic quotient of automorphism group by class-preserving automorphism group is a finite group that is also ... ...
  2 KB (202 words) - 15:16, 17 April 2010
• Transpose-inverse map is class-preserving automorphism for general linear group of degree two iff field has size two
  ==Statement== The transpose-inverse map for the general linear group of degree two over a field F is a class-preserving automorphism if and only ... ...
  473 bytes (69 words) - 17:35, 12 January 2014
• Class-preserving automorphism group of finite p-group is p-group
  ==Statement== Suppose P is a finite p-group, i.e., a fact about::group of prime power order where the prime is p. Let \operatorname{Class}(P) ... ...
  670 bytes (102 words) - 17:26, 26 September 2008

Page text matches

• Question:Inner automorphisms preserving conjugacy classes
  Question: An inner automorphism sends every element to within its conjugacy class. Are there outer automorphisms that do so? Answer: Yes. An automorphism ... ...
  1 KB (168 words) - 22:53, 1 April 2011
• Group in which every class-preserving automorphism is inner
  ==Definition== A group in which every class-preserving automorphism is inner is a group with the property that any defining ingredient::class ... ...
  1,006 bytes (121 words) - 19:44, 1 October 2008
• Class-preserving implies IA
  ==Statement== ===Property-theoretic statement=== The automorphism property of being a fact about::class-preserving automorphism is stronger than ... ...
  874 bytes (106 words) - 20:24, 9 August 2008
• Inner implies class-preserving
  ==Statement== ===Property-theoretic statement=== The automorphism property of being an inner automorphism is stronger than, or implies, the automorphism ... ...
  2 KB (364 words) - 20:26, 9 August 2008
• Linearly pushforwardable implies class-preserving for class-separating field
  ==Statement== In a fact about::class-separating field, any fact about::linearly pushforwardable automorphism is class-preserving. ==Definitions used== ... ...
  2 KB (348 words) - 20:44, 25 April 2009
• Universal power not implies class-preserving
  ==Statement== A universal power automorphism of a group (i.e., an automorphism obtained by taking the n^{th} power for some integer n) need not ... ...
  1 KB (148 words) - 11:50, 5 September 2008
• Class-preserving implies linearly pushforwardable
  ==Statement== Suppose G is a group and k is a fact about::class-determining field for G. Then, any fact about::class-preserving automorphism of ... ...
  4 KB (564 words) - 20:26, 9 August 2008
• Hall-extensible implies class-preserving
  ==Statement== Any Hall-extensible automorphism of a finite group is a class-preserving automorphism. ==Definitions used== ===Hall-extensible automorphism ... ...
  2 KB (256 words) - 01:21, 1 May 2009
• Rational class-preserving automorphism
  ==Definition== An automorphism \sigma of a group G is termed a rational class-preserving automorphism if it satisfies the following equivalent ... ...
  936 bytes (112 words) - 00:00, 4 September 2009
• Class-preserving implies linearly extensible
  ==Definition== Let G be a group, and k a class-determining field for it. Then, any class-preserving automorphism of G is linearly extensible. ... ...
  590 bytes (73 words) - 20:25, 9 August 2008
• Subgroup-conjugating not implies class-preserving
  ==Statement== A subgroup-conjugating automorphism of a group (i.e., an automorphism that sends every subgroup to a conjugate subgroup) need not ... ...
  987 bytes (102 words) - 12:00, 5 September 2008
• 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
• Conjugacy-separable implies every quotient-pullbackable automorphism is class-preserving
  ==Statement== In a conjugacy-separable group, every fact about::quotient-pullbackable automorphism is a fact about::class-preserving automorphism. ... ...
  687 bytes (62 words) - 18:39, 27 April 2009
• Finite solvable-extensible implies class-preserving
  ==Statement== Any finite solvable-extensible automorphism of a finite solvable group is a class-preserving automorphism. ==Definitions used== ... ...
  2 KB (287 words) - 19:16, 30 May 2009
• Group in which every automorphism is class-preserving
  ==Definition== A group is termed a group in which every automorphism is class-preserving if it satisfies the following equivalent conditions: ... ...
  1 KB (146 words) - 22:47, 25 June 2011
• Extended class-preserving automorphism
  ==Definition== An automorphism \sigma of a group G is termed an extended class-preserving automorphism if it sends every element either to an ... ...
  649 bytes (76 words) - 23:49, 1 September 2009
• Transitively normal not implies conjugacy-closed normal
  ==Statement== A transitively normal subgroup of a group (a subgroup with the property that every normal subgroup of it is normal in the whole ... ...
  4 KB (622 words) - 19:37, 5 September 2008
• 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
• Finite group with cyclic quotient of automorphism group by class-preserving automorphism group
  ==Definition== A finite group with cyclic quotient of automorphism group by class-preserving automorphism group is a finite group that is also ... ...
  2 KB (202 words) - 15:16, 17 April 2010
• Class-preserving automorphism group of finite p-group is p-group
  ==Statement== Suppose P is a finite p-group, i.e., a fact about::group of prime power order where the prime is p. Let \operatorname{Class}(P) ... ...
  670 bytes (102 words) - 17:26, 26 September 2008