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The multiplicator of finite nilpotent groups

Published online by Cambridge University Press:  17 April 2009

J. W. Wamsley
J. W. Wamsley
Affiliation:
The Flinders University of South Australia, Bedford Park, South Australia.
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Abstract

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Let G be a group and M a G-module; then d(G) denotes the minimal number of generators of G and dG(M) the minimal number of generators over ZG of M. For G a finite nilpotent group let G = F/R, F free, be a presentation for G; then it is shown that d(R/[F, R]) = dG(R/[R, R]), that is d(G) + d(M(G)) = dG(R/R′), where M(G) denotes the Schur multiplicator of G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 3 , Issue 1 , August 1970 , pp. 1 - 8
Copyright
Copyright © Australian Mathematical Society 1970

References

[1] Lyndon, Roger C., “Cohomology theory of groups with a single defining relation”, Ann. of Math. (2) 52 (1950), 650–665.CrossRefGoogle Scholar
[2] Neumann, B.H., “On some finite groups with trivial multiplicator”, Publ. Math. Debrecen 4 (1956), 190–194.Google Scholar
[3] Schur, J., “Untersuchungen über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen”, J. Reins. Angew. Math. 132 (1907), 85–137.Google Scholar
[4] Swan, Richard G., “Minimal resolutions for finite groups”, Topology 4 (1965), 193–208.CrossRefGoogle Scholar