$2$-Blocks with minimal nonabelian defect groups III

Benjamin Sambale

Vol. 280 (2016), No. 2, 475–487

DOI: 10.2140/pjm.2016.280.475

Abstract

We prove that two $2$-blocks of (possibly different) finite groups with a common minimal nonabelian defect group and the same fusion system are isotypic (and therefore perfectly isometric) in the sense of Broué. This continues former work by Cabanes and Picaronny (J. Fac. Sci. Univ. Tokyo Sect. IA Math. 39:1 (1992), 141–161), Sambale (J. Algebra 337 (2011), 261–284) and Eaton et al. (J. Group Theory 15:3 (2012), 311–321).

Keywords

minimal nonabelian defect groups, perfect isometries, isotypies

Mathematical Subject Classification 2010

Primary: 20C15, 20C20

Milestones

Received: 26 April 2015

Revised: 6 June 2015

Accepted: 7 June 2015

Published: 28 January 2016