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GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II

Published online by Cambridge University Press:  30 March 2012

HOWARD SMITH
HOWARD SMITH*
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, U.S.A. e-mail: [email protected]
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Abstract

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It is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a π-group for some finite set π of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.

Keywords

20E1520F19
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 3 , September 2012 , pp. 529 - 534
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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