Algebra & Number Theory

A 2-block splitting in alternating groups

Christine Bessenrodt

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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.

Article information

Source
Algebra Number Theory, Volume 3, Number 7 (2009), 835-846.

Dates
Received: 9 December 2008
Revised: 4 August 2009
Accepted: 5 August 2009
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513797484

Digital Object Identifier
doi:10.2140/ant.2009.3.835

Mathematical Reviews number (MathSciNet)
MR2579397

Zentralblatt MATH identifier
1182.20010

Subjects
Primary: 20C15: Ordinary representations and characters
Secondary: 20C20: Modular representations and characters 20C30: Representations of finite symmetric groups

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

Citation

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


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References

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