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Finite potent groups

Published online by Cambridge University Press:  17 April 2009

John Poland
John Poland
Affiliation:
Department of Mathematics and Statistics, Carleton University, Ottawa, CanadaK1S 5B6.
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Abstract

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A group is potent if for any element of the group and any prescribed positive integer (dividing its order if this order is finite) there corresponds a finite homomorphic image of the group in which the element has the prescribed integer as its order. The finite potent groups form a finite variety that contains all finite nilpotent groups, all finite metabelian groups, and precisely one simple group, A5.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 23 , Issue 1 , February 1981 , pp. 111 - 120
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Huppert, B., Endliahe Gruppen I (Die Grundlehren der mathematischen Wissenschaften, 134. Springer-Verlag, Berlin, Heidelberg, New York, 1967).Google Scholar
[2]Lennox, J.C. and Rhemtulla, A.H., “On the potency of finitely generated soluble groups”, preprint, 1980.Google Scholar
[3]Schenkman, Eugene, Group theory (Van Nostrand, Princeton, New Jersey; Toronto; London; 1965).Google Scholar
[4]Suzuki, Michio, “Finite groups with nilpotent centralizers”, Trans. Amer. Math. Soc. 99 (1961), 425–470.Google Scholar