Extensible local isomorphism

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Revision as of 02:32, 25 February 2009 by Vipul (talk | contribs) (New page: {{termrelatedto|Extensible automorphisms problem}} ==Definition== Suppose <math>G</math> is a group, <math>A</math> and <math>B</math> are subgroups of <math>G</math>, and <math>\sigma:A...)
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This term is related to: Extensible automorphisms problem
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Definition

Suppose G is a group, A and B are subgroups of G, and \sigma:A \to B is an isomorphism of groups. We say that \sigma is an extensible local isomorphism if, for any group K containing G, there exists an automorphism \alpha of K such that the restriction of \alpha to A equals \sigma.

The extensible local isomorphisms conjecture states that an isomorphism of subgroups of G is an extensible local isomorphism if and only if it can be extended to an inner automorphism of G. This is a strong version of the extensible automorphisms conjecture.