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BARELY TRANSITIVE AND HEINEKEN MOHAMED GROUPS

Published online by Cambridge University Press:  01 April 1997

V. V. BELYAEV  and
M. KUZUCUOĞLU
V. V. BELYAEV
Affiliation:
Krasnoyarsk Engineering Building Institute (KISI), Krasnoyarsk 660041, Russia. E-mail: [email protected]
M. KUZUCUOĞLU
Affiliation:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey. E-mail: [email protected]
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Abstract

A negative answer to the Kuroš–Černikov Question 21 in [7], whether a group satisfying the normalizer condition is hypercentral, was given by Heineken and Mohamed in 1968 [6]. They constructed groups G satisfying:

(i) G is a locally finite p-group for a prime p,

(ii) G/G′≅Cp∞ and G′ is countable elementary abelian,

(iii) every proper subgroup of G is subnormal and nilpotent,

(iv) Z(G)={1},

(v) the set of normal subgroups of G contained in G′ is linearly ordered by set inclusion, see [3, p. 334],

(vi) KG′ is a proper subgroup in G for every proper subgroup K of G, see [6, Lemma 1(a)].

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 261 - 263
Copyright
The London Mathematical Society 1997

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