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Vipul at 02:31, 21 July 2007

2007-07-21T02:31:16Z

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{{automorphism property}}

{{variationof|pushforwardable automorphism}}

{{variationof|extensible automorphism}}

{{termrelatedto|Extensible automorphisms problem}}

{{wikilocal}}

==Definition==

===Definition with symbols===

Let <math>G</math> be a group and <math>\sigma</math> an automorphism of <math>G</math>. <math>\sigma</math> is said to be '''CS-pushforwardable''' if for any homomophism <math>\rho:G \to Aut(N)</math> where <math>N</math> is a [[characteristically simple group]], there exists an inner automorphism <math>\phi</math> of </math>Aut(N)</math> such that <math>\phi \circ \rho = \rho \circ \sigma</math>.

==Relation with other properties==

===Stronger properties===

* [[Extensible automorphism]]
* [[Semidirecty extensible automorphism]]
* [[Potentially characteristic-semidirectly extensible automorphism]]: The implication is a consequence of the [[automorphism group action lemma]]

===Weaker properties===

* [[CS-extensible automorphism]]

CS-pushforwardable automorphism - Revision history

Vipul: 1 revision

Vipul at 02:31, 21 July 2007