A 2-block splitting in alternating groups

Bessenrodt, Christine

doi:10.2140/ant.2009.3.835

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A 2-block splitting in alternating groups

Christine Bessenrodt

Vol. 3 (2009), No. 7, 835–846

DOI: 10.2140/ant.2009.3.835

Abstract

In 1956, Brauer showed that there is a partitioning of the $p$ -regular conjugacy classes of a group according to the $p$ -blocks of its irreducible characters with close connections to the block theoretical invariants. In a previous paper, the first explicit block splitting of regular classes for a family of groups was given for the 2-regular classes of the symmetric groups. Based on this work, the corresponding splitting problem is investigated here for the 2-regular classes of the alternating groups. As an application, an easy combinatorial formula for the elementary divisors of the Cartan matrix of the alternating groups at $p = 2$ is deduced.

Keywords

alternating groups, $p$-regular conjugacy classes, irreducible characters, Brauer characters, $p$-blocks, Cartan matrix

Mathematical Subject Classification 2000

Primary: 20C15

Secondary: 20C20, 20C30

Milestones

Received: 9 December 2008

Revised: 4 August 2009

Accepted: 5 August 2009

Published: 29 November 2009

Authors

Christine Bessenrodt
Institut für Algebra, Zahlentheorie und Diskrete Mathematik Fakultät für Mathematik und Physik Leibniz Universität Hannover Welfengarten 1 D-30167 Hannover Germany
http://www-ifm.math.uni-hannover.de/~bessen/

Vol. 3, No. 7, 2009