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HYPERCENTRAL GROUPS WITH ALL SUBGROUPS SUBNORMAL III

Published online by Cambridge University Press:  23 October 2001

HOWARD SMITH
HOWARD SMITH
Affiliation:
Department of Mathematics, Bucknell University, Lewisburg, PA 17837, U.S.A.howsmith@bucknell.edu
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Abstract

It is shown that a hypercentral group that has all subgroups subnormal and every non-nilpotent subgroup of bounded defect is nilpotent. As a consequence, a hypercentral group of length at most ω in which every subgroup is subnormal is nilpotent.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 33 , Issue 5 , September 2001 , pp. 591 - 598
Copyright
© The London Mathematical Society 2001

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