UNITS IN Fq k (Cp or Cq)

Abstract

Abstract. Let q be a prime, F q k be a finite field having q k elements and Cn r Cq be a group with presentation a, b | a n , b q , b −1 ab = a r , where (n, rq) = 1 and q is the multiplicative order of r modulo n. In this paper, we address the problem of computing the Wedderburn decomposition of the group algebra F q k (Cn r Cq) modulo its Jacobson radical. As a consequence, the structure of the unit group of F q k (Cp r Cq) is obtained when p is a prime different from q.Mathematics Subject Classification (2010): 16U60, 16S34, 20C05

Units in $F(C_n \times Q_{12})$ and $F(C_n \times D_{12})$

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