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Identifieur interne : 002049 ( Main/Exploration ); précédent : 002048; suivant : 002050P
Auteurs : Michiel HazewinkelSource :
- Encyclopaedia of Mathematics
Abstract
Abstract: π-Separable Group - A group which has a normal series such that the order of every factor contains at most one prime from π (π is a set of prime numbers). The class of π-separable groups contains the class of π-solvable groups (cf. π-solvable group). For finite π-separable groups, the π-Sylow properties (cf. Sylow theorems) have been shown to hold (see [1]). In fact, for any set π1 ⊆, a finite π-separable group G contains a π1-Hall subgroup (cf. also Hall subgroup), and any two π1-Hall subgroups are conjugate in G. Any π1-subgroup of a π-separable group G is contained in some π1-Hall subgroup of G (see [2]).
Url:
DOI: 10.1007/978-94-015-1237-4_2
Affiliations:
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