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On non-nilpotent groups with all subgroups subnormal. (English) Zbl 1097.20512
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.

MSC:
20E15 Chains and lattices of subgroups, subnormal subgroups
20F19 Generalizations of solvable and nilpotent groups
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