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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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