Algebra & Number Theory
- Algebra Number Theory
- Volume 5, Number 8 (2011), 1063-1068.
Involutions, weights and $p$-local structure
We prove that for an odd prime , a finite group with no element of order has a -block of defect zero if it has a non-Abelian Sylow -subgroup or more than one conjugacy class of involutions. For , we prove similar results using elements of order in place of involutions. We also illustrate (for an arbitrary prime ) that certain pairs , with a -regular element and a maximal -invariant -subgroup, give rise to -blocks of defect zero of , and we give lower bounds for the number of such blocks which arise. This relates to the weight conjecture of J. L. Alperin.
Algebra Number Theory, Volume 5, Number 8 (2011), 1063-1068.
Received: 9 June 2010
Revised: 22 December 2010
Accepted: 7 June 2011
First available in Project Euclid: 20 December 2017
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Primary: 20C20: Modular representations and characters
Robinson, Geoffrey. Involutions, weights and $p$-local structure. Algebra Number Theory 5 (2011), no. 8, 1063--1068. doi:10.2140/ant.2011.5.1063. https://projecteuclid.org/euclid.ant/1513729733