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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
##### Keywords:
subnormal subgroups; hypercentral groups