Details
| Original language | English |
|---|---|
| Pages (from-to) | 835-846 |
| Number of pages | 12 |
| Journal | Algebra and Number Theory |
| Volume | 3 |
| Issue number | 7 |
| Publication status | Published - 29 Nov 2009 |
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, Brauer characters, Cartan matrix, Irreducible characters, P-blocks, P-regular conjugacy classes
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Algebra and Number Theory, Vol. 3, No. 7, 29.11.2009, p. 835-846.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A 2-block splitting in alternating groups
AU - Bessenrodt, Christine
PY - 2009/11/29
Y1 - 2009/11/29
N2 - 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.
AB - 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.
KW - Alternating groups
KW - Brauer characters
KW - Cartan matrix
KW - Irreducible characters
KW - P-blocks
KW - P-regular conjugacy classes
UR - http://www.scopus.com/inward/record.url?scp=77954000144&partnerID=8YFLogxK
U2 - 10.2140/ant.2009.3.835
DO - 10.2140/ant.2009.3.835
M3 - Article
AN - SCOPUS:77954000144
VL - 3
SP - 835
EP - 846
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 7
ER -