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Subnomality in soluble minimax groups

Published online by Cambridge University Press:  09 April 2009

D. J. McCaughan
D. J. McCaughan
Affiliation:
Department of mathematics Institute of Advanced Studies Australian National University
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A subgroup H of a group G is said to be subnormal in G if there is a finite chain of subgroups, each normal in its successor, connecting H to G. If such chains exist there is one of minimal length; the number of strict inclusions in this chain is called the subnormal index, or defect, of H in G. The rather large class of groups which have an upper bound for the subnormal indices of their subnormal subgroups has been inverstigated to same extent, mainly with a restriction to solublegroups — for instance, in [10] McDougall considered soluble p-groups in this class. Robinson, in [14], restricted his attention to wreath products of nilpotent groups but extended his investigations to the strictly larger class of groups in which the intersection of any family of subnormal subgroups is a subnormal subgroup. These groups are said to have the subnormal intersection property.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 17 , Issue 1 , February 1974 , pp. 113 - 128
Copyright
Copyright © Australian Mathematical Society 1974

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