IJPAM: Volume 46, No. 2 (2008)

ON THE ORDER OF $\U( {\F}_{p^k} D_{2{p^m}})$

Joe Gildea
Department of Mathematics
National University of Ireland
University Road, Galway, IRELAND
e-mail: joseph.gildea@nuigalway.ie


Abstract.Let $RG$ denote the group ring $G$ of the group $G$ over the ring $R$. Using an established isomorphism between $RG$ and a certain ring of $n \times n$ matrices in conjunction with other techniques, we are able to establish the order of $\U( {\F}_{p^k} D_{2{p^m}})$, where $p$ is an odd prime.

Received: December 18, 2007

AMS Subject Classification: 20C05, 16S34, 15A15, 15A33

Key Words and Phrases: group ring, group algebra, unit group, dihedral

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 2