On computing the minimal number of defining relations for finite groups

Sag, T. W.; Wamsley, J. W.

doi:10.1090/S0025-5718-1973-0364465-8

On computing the minimal number of defining relations for finite groups
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by T. W. Sag and J. W. Wamsley PDF

Math. Comp. 27 (1973), 361-368 Request permission

Abstract:

This paper describes a method for computing the Schur multiplicator of a finite supersolvable group G, given by some fixed generating system chosen from a cyclic series for G, and hence a lower bound for the minimal number of relations needed to define G.

References

J. Reine Angew. Math.

Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215
Gordon H. Bradley, Algorithms for Hermite and Smith normal matrices and linear Diophantine equations, Math. Comp. 25 (1971), 897–907. MR 301909, DOI 10.1090/S0025-5718-1971-0301909-X
Marshall Hall Jr. and James K. Senior, The groups of order $2^{n}\,(n\leq 6)$, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1964. MR 0168631

J. Austral. Math. Soc.

J. W. Wamsley, The deficiency of wreath products of groups, J. Algebra 27 (1973), 48–56. MR 376884, DOI 10.1016/0021-8693(73)90164-6