Abstract. In continuation to the investigation initiated by Ferraz, Goodaire and Milies in [4], we provide an explicit description for the Wedderburn decomposition of finite semisimple group algebras of the class of finite groups G, such that G/Z(G) ∼ = C 2 × C 2 , where Z(G) denotes the center of G.
Let 𝔽qD2N be the group algebra of D2N, the dihedral group of order 2N, over 𝔽q = GF (q). In this paper, we compute the order of the unitary subgroup of the group of units of 𝔽2kD2N with respect to the canonical involution ∗.
Let [Formula: see text] be a generalized dihedral group of order 2n and 𝔽q be a finite field having q elements. In this note, we establish the structure of the unit group of [Formula: see text] for any odd n ≥ 3. This extends a result due to Kaur and Khan [Units in 𝔽2D2p, J. Algebra Appl. 13(2) (2014) 9pp., doi: 10.1142/S0219498813500904] as well as a result due to the authors [Units in 𝔽2kD2n, Int. J. Group Theory 3(3) (2014) 25–34].
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
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.