title
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Computing 2-cocycles for central extensions and relative difference sets

Authors
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D.L. Flannery
Department of Mathematics, National University of Ireland, 
Galway, Ireland 

E.A. O'Brien
Department of Mathematics, University of Auckland,
Private Bag 92019, Auckland, New Zealand

Abstract
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 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.

Status
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Appeared: Comm. Algebra 28 (4), 1939--1955, 2000.