Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 835-846 |
| Seitenumfang | 12 |
| Fachzeitschrift | Algebra and Number Theory |
| Jahrgang | 3 |
| Ausgabenummer | 7 |
| Publikationsstatus | Veröffentlicht - 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.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Algebra und Zahlentheorie
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in: Algebra and Number Theory, Jahrgang 3, Nr. 7, 29.11.2009, S. 835-846.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › 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 -