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Clifford theory for p-sections of finite groups. (English) Zbl 0667.20003

In the paper under review the author is mainly interested in the following situation: K is a field of prime characteristic p and N is a normal subgroup of the finite group G such that G/N is a p-group. He proves that in this case, for any simple KN-module W, there is a unique (up to isomorphism) simple KG-module V such that W is a composition factor of \(V_ N\). Moreover, if W is G-stable then \(V_ N=W\). Similarly, for any block b of N, there is a unique block B of G covering b. These results are known for the case where K is a splitting field; but, as the author shows, this hypothesis is unnecessary.
Reviewer: B.Külshammer

MSC:

20C05 Group rings of finite groups and their modules (group-theoretic aspects)
20C20 Modular representations and characters
16S34 Group rings
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