New York Journal of Mathematics
Volume 12 (2006) 169-182


Cornelia Minette Busch

Conjugacy classes of p-torsion in symplectic groups over S-integers

Published: July 26, 2006
Keywords: Representation theory, cohomology theory
Subject: 20G05, 20G10

For any odd prime p we consider representations of a group of order p in the symplectic group Sp(p-1,Z[1/n]) of (p-1)×(p-1)-matrices over the ring Z[1/n], 0≠ n∈N. We construct a relation between the conjugacy classes of subgroups P of order p in the symplectic group and the ideal class group in the ring Z[1/n] and we use this relation for the study of these conjugacy classes. In particular we determine the centralizer C(P) and N(P)/C(P) where N(P) denotes the normalizer.


Research supported by a grant "Estancias de jóvenes doctores y tecnólogos extranjeros en Espana" (SB 2001-0138) from the Ministerio de Educación, Cultura y Deporte.

Author information

Katholische Universität Eichstätt-Ingolstadt, MGF, D-85071 Eichstätt, Germany