Abstract. The structure of the unit groups of the group algebra of the group ${C_3}^2 \rtimes C_2$ over any field of characteristic $3$ is established in terms of split extensions of cyclic groups.

AMS Subject Classification (1991): 16U60, 16S34, 20C05, 15A33

Keyword(s): unit group, group ring, group algebra, cyclic

Received October 3, 2009, and in revised form September 8, 2010. (Registered under 259/2009.)