Premium
The orbit space of a fusion system is contractible
Author(s) -
Linckelmann Markus
Publication year - 2009
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdn029
Subject(s) - contractible space , mathematics , conjecture , isomorphism (crystallography) , combinatorics , block (permutation group theory) , prime (order theory) , space (punctuation) , orbit (dynamics) , pure mathematics , group (periodic table) , set (abstract data type) , discrete mathematics , algebra over a field , computer science , physics , programming language , chemistry , quantum mechanics , crystal structure , engineering , crystallography , aerospace engineering , operating system
Given a fusion system ℱ on a finite p ‐group P , where p is a prime, we show that the partially ordered set of isomorphism classes in ℱ of chains of non‐trivial subgroups of P , considered as topological space, is contractible, further generalising Symonds’, proof [ Comment. Math. Helvet. 73 (1998) 400–405] of a conjecture of Webb [ Comment. Math. Helvet. 66 (1991) 34–69; Arcata Conference on Representations of Finite Groups, part I, Proceedings of Symposia in Pure Mathematics 47 349–365] and its generalisation to non‐trivial Brauer pairs associated with a p ‐block by Barker [ J. Algebra 212 (1999) 460–465].