Algebra & Number Theory
- Algebra Number Theory
- Volume 3, Number 7 (2009), 835-846.
A 2-block splitting in alternating groups
In 1956, Brauer showed that there is a partitioning of the -regular conjugacy classes of a group according to the -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 is deduced.
Algebra Number Theory, Volume 3, Number 7 (2009), 835-846.
Received: 9 December 2008
Revised: 4 August 2009
Accepted: 5 August 2009
First available in Project Euclid: 20 December 2017
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Bessenrodt, Christine. A 2-block splitting in alternating groups. Algebra Number Theory 3 (2009), no. 7, 835--846. doi:10.2140/ant.2009.3.835. https://projecteuclid.org/euclid.ant/1513797484