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Power and commutator structure of groups

Published online by Cambridge University Press:  17 April 2009

David Shield*
Affiliation:
Goroka Teachers College, Goroka, Papua New Guinea.
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Abstract

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The purpose of this paper is to prove a result about the power and commutator structure of groups which generalises some results of Philip Hall. The results presented here are the key to determining the class of a nilpotent wreath product.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1977

References

[1] Berge, Claude, Graphs and hypergraphs (translated by Minieka, Edward. North-Holland Mathematical Library, 6. North-Holland, Amsterdam, London; American Elsevier, New York, 1973).Google Scholar
[2] Cohn, P. M., Universal algebra (Harper and Row, New York, Evanston, and London, 1965).Google Scholar
[3] Haebich, William, “The multiplicator of various products of groups”, (PhD thesis, Australian National University, Canberra, 1972); see also: abstract, Bull. Austral. Math. Soa. 7 (1972), 461462.CrossRefGoogle Scholar
[4] Hall, P., “A contribution to the theory of groups of prime-power order”, Proc. London Math. Soc. (2) 36 (1934), 2995.CrossRefGoogle Scholar
[5] Huppert, B., Endliche Gruppen I (Die Grundlehren der mathematischen Wissenschaften, 134. Springer-Verlag, Berlin, Heidelberg, New York, 1967).CrossRefGoogle Scholar
[6] Shield, David, “The class of a nilpotent wreath product”, Bull. Austral. Math. Soc. 17 (1977), 5389.CrossRefGoogle Scholar
[7] Ward, M.A., “Basic commutators”, Philos. Trans. Roy. Soc. London Ser. A 264 (1969), 343412.Google Scholar