IJPAM: Volume 49, No. 4 (2008)

ON THE ORDER OF $\U( {\mathbb{F}}_{2^k} D_{10})$ WHEN $5\,\vert\,(2^k-1)$

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

Abstract.Let $\U(RG)$ denote the unit group of the group ring $G$ 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 $\U( {\mathbb{F}}_{2^k} D_{10})$ when $5\,\vert\,(2^k-1)$.

Received: August 14, 2008

AMS Subject Classification: 05C25

Key Words and Phrases: unit group of the group ring, LAGUNA package,

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 49
Issue: 4