Praefrattinigruppen und Matroide. (Prefrattinigroups and matroids)
type: Item
instance of: scholarly article
title: Praefrattinigruppen und Matroide. (Prefrattinigroups and matroids)
zbMATH Open document ID: 0734.20009
DOI: 10.1007/BF03323194
author: Michael Weidner
published in: Results in Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Author's English summary: For finite, solvable groups G, the set M(G) of all maximal subgroups, together with a natural independence relation, forms a matroid. So all bases have the same length. The intersection over one basis is conjugate to the intersection over any other basis. It turns out, that such intersections are prefrattini subgroups, introduced by W. Gaschütz. So we have a canonical description of these subgroups. We construct all epimorphism invariant conjugation classes of subgroups, such that each subgroup (of the class) is an intersection of maximal subgroups (of G). The prefrattini subgroups build the `smallest' class.
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 4214245
zbMATH Keywords: finite, solvable groups
zbMATH Keywords: maximal subgroups
zbMATH Keywords: matroid
zbMATH Keywords: prefrattini subgroups
zbMATH Keywords: intersection of maximal subgroups
MaRDI profile type: Publication
cites work: Pre-Frattini groups.
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description: scientific article; zbMATH DE number 4214245