Abstract
In this article, some nontrivial 2-cocycles are computed for crossed products of algebraic extensions of the field of rational numbers Q with cyclic groups of order 2 and 3, with finite groups of order 4, 6 and 8. The 2-cocycles are applied for bilinear forms over finite-dimensional vector space whose scalars field is Q and few examples of these cocycles are presented in terms of matrices.
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