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GROUPS IN WHICH ALL SUBGROUPS OF INFINITE RANK ARE SUBNORMAL

Published online by Cambridge University Press:  15 January 2004

LEONID A. KURDACHENKO  and
HOWARD SMITH
LEONID A. KURDACHENKO
Affiliation:
Algebra Department, Dnepropetrovsk University, Vul. Naukova 13, Dnepropetrovsk 50, Ukraine 49000
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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Let $G$ be a locally soluble-by-finite group in which every non-subnormal subgroup has finite rank. It is proved that either $G$ has finite rank or $G$ is soluble and locally nilpotent (and even a Baer group). On the other hand, a group $G$ is constructed that has infinite rank and satisfies the given hypothesis, but does not have every subgroup subnormal.

Keywords

20E1520F19
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 46 , Issue 1 , January 2004 , pp. 83 - 89
Copyright
2004 Glasgow Mathematical Journal Trust