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The subnormal structure of metanilpotent groups

Published online by Cambridge University Press:  17 April 2009

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

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Let G be a group with a normal nilpotent subgroup N such that G/N is periodic and nilpotent. If G(p)/N is the Sylow p-subgroup of G/N and Q(p) is the maximal p-radicable subgroup of N, it is shown that G has a bound on the subnormal indices of its subnormal subgroups if and only if there is a positive integer c such that G(p)/Q(p) is nilpotent of class at most c, for all primes p. It is also shown that if G is a periodic metanilpotent group and Q is its maximal radicable abelian normal subgroup then G has a bound on its subnormal indices if and only if there is a positive integer c such that for all primes p the Sylow p-subgroups of G/Q are nilpotent of class at most c.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 6 , Issue 2 , April 1972 , pp. 287 - 306
Copyright
Copyright © Australian Mathematical Society 1972

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