On computing the minimal number of defining relations for finite groups

Authors:
T. W. Sag and J. W. Wamsley

Journal:
Math. Comp. **27** (1973), 361-368

MSC:
Primary 20F05

DOI:
https://doi.org/10.1090/S0025-5718-1973-0364465-8

MathSciNet review:
0364465

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Abstract | References | Similar Articles | Additional Information

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*.

**[1]**J. Schur, "Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen,"*J. Reine Angew. Math.*, v. 132, 1907, pp. 85-137.**[2]**M. Hall, Jr.,*The Theory of Groups*, Macmillan, New York, 1959. MR**21**#1996. MR**0103215 (21:1996)****[3]**G. H. Bradley, "Algorithms for Hermite and Smith normal form matrices,"*Math. Comp.*, v. 25, 1971, pp. 897-907. MR**0301909 (46:1064)****[4]**M. Hall, Jr. & J. K. Senior,*The Groups of Order*, Macmillan, New York, 1964. MR**29**#5889. MR**0168631 (29:5889)****[5]**T. W. Sag & J. W. Wamsley, "Minimal presentations for groups of order ,"*J. Austral. Math. Soc.*(To appear.)**[6]**J. W. Wamsley, "The deficiency of wreath products of groups,"*J. Algebra*. (To appear.) MR**0376884 (51:13059)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0364465-8

Keywords:
Finite supersolvable groups,
relations,
generators,
Schur multiplicator,
minimal

Article copyright:
© Copyright 1973
American Mathematical Society