Barely transitive and Heineken Mohamed groups

Date

1997-04-01

Author

Belyaev, VV
Kuzucuoğlu, Mahmut

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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)].

URI

https://hdl.handle.net/11511/41814

Journal

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

DOI

https://doi.org/10.1112/s0024610797004870

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Department of Mathematics, Article

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Citation Formats

V. Belyaev and M. Kuzucuoğlu, “Barely transitive and Heineken Mohamed groups,” JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, pp. 261–263, 1997, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41814.