Smith, Howard On non-nilpotent groups with all subgroups subnormal. (English) Zbl 1097.20512 Ric. Mat. 50, No. 2, 217-221 (2001). Here is the main result: there is a hypercentral group \(G\) such that: (1) \(G\) is not nilpotent, (2) the torsion subgroup \(T\) of \(G\) is the direct product of finite elementary Abelian \(p\)-groups for different primes \(p\), (3) \(G/T\) is Abelian of infinite rank, (4) every subgroup of \(G\) of finite torsionfree rank is nilpotent, (5) every subgroup of \(G\) is subnormal. Reviewer: L. N. Vaserstein (University Park) Cited in 2 Documents MSC: 20E15 Chains and lattices of subgroups, subnormal subgroups 20F19 Generalizations of solvable and nilpotent groups Keywords:subnormal subgroups; hypercentral groups PDFBibTeX XMLCite \textit{H. Smith}, Ric. Mat. 50, No. 2, 217--221 (2001; Zbl 1097.20512)