Vol.09 Issue-02, (July - December, 2017) ISSN: 2394-9309 (E) / 0975-7139 (P) Aryabhatta Journal of Mathematics and Informatics (Impact Factor- 5.856) Double-Blind Peer Reviewed Refereed Open Access International e-Journal - Included in the International Serial Directories Aryabhatta Journal of Mathematics and Informatics http://www.ijmr.net.in email id- irjmss@gmail.com Page 106 Primitive central idempotents of certain finite semisimple group algebras Shalini Gupta Department of Mathematics, Punjabi University, Patiala, India. Abstract The objective of this paper is to give a complete algebraic structure of semisimple group algebras of some finite indecomposable groups, whose central quotient is the Klein’s four group, over a finite field. Keywords: semisimple group algebra, metabelian groups , indecomposable groups, primitive central idempotents, Wedderburn decomposition. MSC2000: 16S34; 20C05; 16K20 1. Introduction Let q be a finite field with q elements and G be a finite group of order coprime to q, so that the group algebra   [] is semisimple. The most important problem in the area of group algebras is to find a complete set of primitive central idempotents of semisimple group algebra   []. The knowledge of primitive central idempotents is useful in finding Wederburn decomposition, unit group of integral group ring, various parameters in error correcting codes [1,2,4,5,10,11,13,14,15,16,17,18]. In [3], Bakshi et.al. obtained a complete algebraic structure of   [], G metabelian, using Strong Shoda pairs. They further illustrated their result by providing a complete set of primitive central idempotents and the Wedderburn decomposition of certain finite group algebras of indecomposable groups whose central quotient is Klein’s four group. Further, Neha et. al. [12] obtained a complete Wedderburn decomposition of group algebras of all such indecomposable groups using the method developed by Ferraz in [6]. In this paper, we give a complete algebraic structure of   [] for some indecomposable groups G, as classified by Milies [7], using the method developed in [3].