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On a result of Johnson about Schur multipliers

Published online by Cambridge University Press:  18 May 2009

James Wiegold
James Wiegold
Affiliation:
School of Mathematics, University of Wales College of Cardiff, Cardiff CF2 4AG
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The purpose of this short note is to give a new and shorter proof of the following theorem of Johnson [1], and to extend it somewhat.

Theorem 1. Let G be a finite non-cyclic p-group possessing a non-empty subset X such that, for each x in X, <X/{x}>G′ is a complement for <x> in G. Then the Schur multiplier of G is non-trivial.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 3 , September 1992 , pp. 347
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

REFERENCES

1.Johnson, David L., A property of finite p-groups with trivial multiplicator, Amer. J. Math. 98 (1976), 105–108.CrossRefGoogle Scholar
2.Wiegold, James, The Schur multiplier: an elementary approach, in Groups—St. Andrews, 1981, London Mathematical Society Lecture Note Series 71 pp. 137–154.Google Scholar