Extension of automorphisms of subgroups. (Q2882501)
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scientific article; zbMATH DE number 6031019
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extension of automorphisms of subgroups. |
scientific article; zbMATH DE number 6031019 |
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6 May 2012
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finite groups
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extensions of automorphisms
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quasi-injective groups
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injective type groups
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automorphism liftings
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0.9494026
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0.94205236
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0.94200546
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0.93820393
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0.9304094
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Extension of automorphisms of subgroups. (English)
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The authors study the finite groups \(G\) that are of ``injective type'', which means that every automorphism of every subgroup of \(G\) can be extended to an automorphism of \(G\).NEWLINENEWLINE This is a complicated class of groups, comprising (and the authors prove this) the group \(A_5\), but not \(\mathrm{SL}(2,5)\). Among the main results, the authors show that a finite non-Abelian group of injective type must have even order (Theorem 2.7) and they also give (Theorem 2.6) a complete description of those finite non-Abelian groups that are in the same time quasi-injective and of injective type.
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