Automorphisms of soluble groups
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Colleges, School and Institutes
Let R be a group of prime order r that acts on the r-group G, let RG be the semidirect product of G with R, let F be a field and V be a faithful completely reducible F[RG]-module. Trivially, CG(R) acts on CV (R). Let K be the kernel of this action. What can be said about K? This question is considered when G is soluble. It turns out that K is subnormal in G or r is a Fermat or half-Fermat prime. In the latter cases, the subnormal closure of K in G is described. Several applications to the theory of automorphisms of soluble groups are given.
|Number of pages||650|
|Journal||London Mathematical Society. Proceedings|
|Publication status||Published - 2016|
- Automophisms, soluble group