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Subnormal structure in some classes of infinite groups

Published online by Cambridge University Press:  17 April 2009

D.J. McCaughan
D.J. McCaughan
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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Let p be a prime and G a group with a p–reduced nilpotent normal subgroup N such that G/N is a nilpotent p–group. It is shown that if G has the subnormal intersection property and if G/N is finite or N is p–torsion-free, then G is nilpotent. This result is used to prove that an abelian-by-finite group has the subnormal intersection property if and only if it has a bound for the subnormal indices of its subnormal subgroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 8 , Issue 1 , February 1973 , pp. 137 - 150
Copyright
Copyright © Australian Mathematical Society 1973

References

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