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Schunk classes are nilpotent product closed

Published online by Cambridge University Press:  17 April 2009

James Wiegold
James Wiegold
Affiliation:
Department of Pure Mathematics, SGS, Australian National University, Canberra. A.C.T. Department of Pure Mathematics, University College, Cardiff, U.K.
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Abstract

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The following result is proved. Let X be a Schunk class and k a positive integer. Then the k–th nilpotent product of any two groups in X¯ is in X¯.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 1 , April 1969 , pp. 27 - 28
Copyright
Copyright © Australian Mathematical Society 1969

References

[1] Golovin, O.N., “Nilpotent products of groups”, Amer. Math. Soc. Transl. (2) 2 (1956), 89–115. Translated from Mat. Sb. N.S. 27 (69) (1950), 427–454.Google Scholar
[2] Wielandt, Helmut, Finite permutation groups (Academic Press, New York, 1964).Google Scholar