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Subnormal structure in some classes of infinite groups
Published online by Cambridge University Press: 17 April 2009
Abstract
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
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