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Computing 2-cocycles for central extensions and relative difference sets. (English) Zbl 0999.20047
Summary: We present an algorithm to compute \(H^2(G,U)\) for a finite group \(G\) and finite Abelian group \(U\) (trivial \(G\)-module). The algorithm returns a generating set for the second cohomology group in terms of representative 2-cocycles, which are given explicitly. This information may be used to find presentations for corresponding central extensions of \(U\) by \(G\). An application of the algorithm to the construction of relative \((4t,2,4t,2t)\)-difference sets is given.

MSC:
20J06 Cohomology of groups
20E22 Extensions, wreath products, and other compositions of groups
20F05 Generators, relations, and presentations of groups
20-04 Software, source code, etc. for problems pertaining to group theory
68W30 Symbolic computation and algebraic computation
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
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