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Ensuring a finite group is supersoluble

Published online by Cambridge University Press:  17 April 2009

R. A. Bryce
R. A. Bryce
Affiliation:
Mathematical Sciences Institute, The Australian National University, Canberra, ACT 0200, Australia
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A special case of the main result is the following. Let G be a finite, non-supersoluble group in which from arbitrary subsets X, Y of cardinality n we can always find x ∈ X and y ∈ Y generating a supersoluble subgroup. Then the order of G is bounded by a function of n. This result is a finite version of one line of development of B.H. Neumann's well-known and much generalised result of 1976 on infinite groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 74 , Issue 2 , October 2006 , pp. 219 - 226
Copyright
Copyright © Australian Mathematical Society 2006

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