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On the solubility of a product of permutable subgroups

Published online by Cambridge University Press:  09 April 2009

John C. Lennox
John C. Lennox
Affiliation:
Mathematics Institute, University College, Cardiff.
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Abstract

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Conditions are investigated under which a product G = HK of soluble subgroups H, K, each permutable in G, is soluble. It is shown in particular that this is true if one of the subgroups is nilpotent or if H ∩ K is subnormal in both H and K.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 2 , September 1976 , pp. 252 - 255
Copyright
Copyright © Australian Mathematical Society 1976

References

Itô, Noboru (1955), ‘Über das Produkt von zwei abelschen Gruppen’, Math. Z. 62, 400–401.CrossRefGoogle Scholar
Iwasawa, Kenkiti (1943), ‘On the structure of infinite M-groups’, Japan. J. Math. 18, 709–728.Google Scholar
Stonehewer, Stewart E. (1972), ‘Permutable subgroups of infinite groups’, Math. Z. 125, 1–16.Google Scholar
Stonehewer, S. E. (1973), ‘Permutable subgroups of some finite p-groups’, J. Austral. Math. Soc. 16, 90–97.CrossRefGoogle Scholar