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The efficiency of PSL(2, p)3 and other direct products of groups

Published online by Cambridge University Press:  18 May 2009

C. M. Campbell ,
I. Miyamoto ,
E. F. Robertson  and
P. D. Williams
C. M. Campbell
Affiliation:
University of St. Andrews, North Haugh, St. Andrews, Fife KY16 9SS, Scotland
I. Miyamoto
Affiliation:
Faculty of Engineering, Yamanashi University, Takeda-4, Kofu, Japan
E. F. Robertson
Affiliation:
University of St. AndrewsNorth Haugh, St. Andrews, Fife KY16 9SS, Scotland
P. D. Williams
Affiliation:
Department of Mathematics, California State University, San BernardinoCalifornia 92407, U.S.A.
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A finite group G is efficient if it has a presentation on n generators and n + m relations, where m is the minimal number of generators of the Schur multiplier M (G)of G. The deficiency of a presentation of G is r–n, where r is the number of relations and n the number of generators. The deficiency of G, def G, is the minimum deficiency over all finite presentations of G. Thus a group is efficient if def G = m. Both the problem of efficiency and the converse problem of inefficiency have received considerable attention recently; see for example [1], [3], [14] and [15].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 39 , Issue 3 , September 1997 , pp. 259 - 268
Copyright
Copyright © Glasgow Mathematical Journal Trust 1997

References

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