A negative answer to the Kuroš–Černikov Question 21 in , whether a group satisfying the normalizer condition is hypercentral, was given by Heineken and Mohamed in 1968 . 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,
(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)].