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Trifactorisable groups

Published online by Cambridge University Press:  17 April 2009

Elizabeth Pennington
Elizabeth Pennington
Affiliation:
Department of Pure Mathematics, Queen Mary College, University of London, London, England.
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Abstract

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The group G is called trifactorisable if G has three subgroups, A, B, and C such that G = AB = BC = CA. Obviously the structure of the group G will be restricted by the structure of these subgroups. In this paper it will be shown that a finite group G is π-separable if and only if it satisfies Dπ and has a trifactorisation with two factors π closed and the third, C say, π-separable. In this case we show that the π- and π′-lengths of G can be at most one more than those of C, and so it is this factor which “controls” the structure of G. Similar results are proved for π-solubility and solubility.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 3 , June 1973 , pp. 461 - 469
Copyright
Copyright © Australian Mathematical Society 1973

References

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