Characterization of a semidirect product of groups by its endomorphism semigroup (Q2709045)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Characterization of a semidirect product of groups by its endomorphism semigroup |
scientific article |
Statements
22 January 2002
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semidirect products of groups
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groups of endomorphisms
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orthogonal idempotents
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summable idempotents
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Characterization of a semidirect product of groups by its endomorphism semigroup (English)
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A semidirect product of groups is characterized using properties of the group of endomorphisms of the group. The characterization allows to give conditions for summability of orthogonal idempotents of the group of endomorphisms (\(x,y\in\text{End }G\) are summable, if the map \(g\to(gx)(gy)\), \(g\in G\) is an endomorphism of \(G\)). It is also established that isomorphism of groups of endomorphisms induces isomorphism of orthogonal summable idempotents.NEWLINENEWLINEFor the entire collection see [Zbl 0954.00028].
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