Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-25T06:12:25.175Z Has data issue: false hasContentIssue false
  • English
  • Français

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: belyaev@home.krasnoyarsk.su
M. KUZUCUOĞLU
Affiliation:
Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey. E-mail: matmah@rorqual.cc.metu.edu.tr
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)