Algebra & Number Theory

Involutions, weights and $p$-local structure

Geoffrey Robinson

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Abstract

We prove that for an odd prime p, a finite group G with no element of order 2p has a p-block of defect zero if it has a non-Abelian Sylow p-subgroup or more than one conjugacy class of involutions. For p=2, we prove similar results using elements of order 3 in place of involutions. We also illustrate (for an arbitrary prime p) that certain pairs (Q,y), with a p-regular element y and Q a maximal y-invariant p-subgroup, give rise to p-blocks of defect zero of NG(Q)Q, and we give lower bounds for the number of such blocks which arise. This relates to the weight conjecture of J. L. Alperin.

Article information

Source
Algebra Number Theory, Volume 5, Number 8 (2011), 1063-1068.

Dates
Received: 9 June 2010
Revised: 22 December 2010
Accepted: 7 June 2011
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513729733

Digital Object Identifier
doi:10.2140/ant.2011.5.1063

Mathematical Reviews number (MathSciNet)
MR2948472

Zentralblatt MATH identifier
1246.20010

Subjects
Primary: 20C20: Modular representations and characters

Keywords
block involution

Citation

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


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