On p-chief factors of finite groups. (English) Zbl 0575.20012
The author uses methods of modular representation theory to characterize p-constrained and p-solvable groups in terms of p-chief factors. For a finite group G and a prime p the principal block of the group algebra FG over the prime field \(F=GF(p)\) plays a central role. The following results are obtained: G is p-constrained iff each irreducible FG-module belonging to the principal block is a composition factor of a suitable tensor product of p-chief factors. G is p-solvable iff the multiplicity of every irreducible FG-module E as a complemented chief factor in a chief series of G equals the multiplicity of E in the second Loewy layer of the principal indecomposable FG-module.
Reviewer: W.Hamernik
MSC:
| 20C20 | Modular representations and characters |
| 20D10 | Finite solvable groups, theory of formations, Schunck classes, Fitting classes, \(\pi\)-length, ranks |
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
Keywords:
p-constrained groups; p-solvable groups; p-chief factors; principal block; group algebra; chief series; Loewy layer; principal indecomposable FG-moduleReferences:
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