Derivations of group rings for finite and FC groups

Derivations of group rings for finite and FC groups

In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, o...

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Veröffentlicht in:Finite fields and their applications 2021-12, Vol.76, p.101921, Article 101921
Hauptverfasser: Arutyunov, A.A., Kosolapov, L.M.
Format: Artikel
Sprache:eng
Schlagworte:
FC-groups
Finite groups
Group algebras
Group rings
Keywords derivations
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Zusammenfassung:In this paper we establish decomposition theorems for derivations of group rings. We provide a topological technique for studying derivations of a group ring A[G] in case G has finite conjugacy classes. As a result, we describe all derivations of algebra A[G] for the case when G is a finite group, or G is an FC-group. In addition, we describe an algorithm to explicitly calculate all derivations of a group ring A[G] in case G is finite. As examples, derivations of Z4[S3] and F2mD2n are considered.
ISSN:1071-5797
1090-2465
DOI:10.1016/j.ffa.2021.101921