Abstract
In this paper we consider the group algebra FG, where G is a non-abelian group and characteristic of the field F does not divides o(G), then FG is semisimple, and hence decomposes into a direct sum of minimal ideals generated by the idempotents we give the explicit expressions for the linear and non linear idempotents in the group algebra of nonabelian groups: generalized quaternion group Q4n of order 4n for every n, V8n of order 8n where n is odd, and the group U6n. We also describe (4n, 4n−1, 2), (4n, 4n−2, 2), (4n, 4n−3, 2), (4n, 4n−4, 2) group codes. Codes over Q12 and V24 are also obtained.
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