#### Vol. 3, No. 7, 2009

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A 2-block splitting in alternating groups

### Christine Bessenrodt

Vol. 3 (2009), No. 7, 835–846
##### 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