On a conjecture of Webb
type: Item
instance of: scholarly article
title: On a conjecture of Webb
zbMATH Open document ID: 0714.20012
DOI: 10.1007/BF01191872
author: Jacques Thévenaz
published in: Archiv der Mathematik
publication date: 1992-01-01T00:00:00Z
review text: Let \(\Delta\) be the simplicial complex of chains of non-trivial p- subgroups of a finite group G, for some prime divisor p of \(| G|\). A conjecture of Webb asserts that the orbit complex \(\Delta\) /G is contractible. In the present note, the conjecture is proved when G satisfies one of the following conditions: (a) G is p-solvable, (b) G has a Sylow p-subgroup which is either abelian, or generalized quaternion, or TI. The proofs are based on some elementary results on p-subgroups and control of fusion.
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 55U10
zbMATH DE Number: 4175233
zbMATH Keywords: chains of p-subgroups
zbMATH Keywords: simplicial complex of chains
zbMATH Keywords: finite group
zbMATH Keywords: orbit complex
zbMATH Keywords: p-solvable
zbMATH Keywords: Sylow p-subgroup
zbMATH Keywords: fusion
Wikidata QID: Q123347086
MaRDI profile type: Publication
cites work: Projectives in Burnside rings, projectives in Green rings, and generalized Steinberg modules.
cites work: Some Remarks on a Conjecture of Alperin
cites work: On group homomorphisms inducing mod-\(p\) cohomology isomorphisms
cites work: Homotopy properties of the poset of nontrivial p-subgroups of a group
cites work: Homotopy equivalence of posets with a group action
cites work: A local method in group cohomology
cites work: Q3794385
cites work: A split exact sequence of Mackey functors
full work available at URL: https://doi.org/10.1007/bf01191872
OpenAlex ID: W1564391209
Recommended article: On a conjecture of J. Weidmann
Recommended article: A NOTE ON THE WEISS CONJECTURE
Recommended article: A Note on Weinstein's Conjecture
Recommended article: On the Weiss conjecture. I
Recommended article: On a theorem of Weiss
Recommended article: Q4528501
Recommended article: On a conjecture of Watkins
Recommended article: On a conjecture of W. Bergweiler
Recommended article: On a conjecture of W. Veys
description: scientific article; zbMATH DE number 4175233