On the connectivity of the subpair complex of a block,

by Charles W. Eaton


Abstract:

We demonstrate that the simplicial complex formed from the poset of 
non-trivial subpairs for a given $p$-block of a finite group $G$ is 
disconnected if and only if $G$ has the block analogue of a 
strongly $p$-embedded subgroup.

Status: Accepted for publication in Journal of Algebra.


School of Mathematics and Statistics
University of Birmingham
Edgbaston
Birmingham
B15 2TT
England