IJPAM: Volume 73, No. 2 (2011)
THE UNIT GROUPS OF
OF GROUPS WITH ORDER 12

Tang Gaohua
, Gao Yanyan
School of Mathematical Sciences
Guangxi Teachers Education University
Nanning, Guangxi 530023, P.R. CHINA


School of Mathematical Sciences
Guangxi Teachers Education University
Nanning, Guangxi 530023, P.R. CHINA
Abstract. Note that there are five mutually non-isomorphic groups of order 12: two decomposable Abelian groups
and
; three indecomposable non-Abelian groups
,
and
. For a finite field
, the structure of
was determined by R.K. Sharma, J.B. Srivastava and M. Khan in 2007. In this paper, we determine the structure of the unit group
of the group ring
, where
is a finite field, and
=
,
,
or
.
Received: June 13, 2011
AMS Subject Classification: 16S34, 16U60, 20C05
Key Words and Phrases: finite field, group ring, unit group
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 73
Issue: 2