Local nilpotent groups satisfying a weak condition of minimality or maximality for subgroups of fixed degree of nilpotency - Onishchuk , V. A.; Sysak , Ya. P. (Ukrains’kyi Matematychnyi Zhurnal, 1992)
We study locally nilpotent groups containing subgroups of class c, c>1, and satisfying the weak maximum condition or the weak minimum condition on с-nilpotent subgroups. It is proved that nilpotent groups of this type are minimax and periodic locally nilpotent groups of this type are Chernikov groups. It is also proved that if a group G is either nilpotent or periodic locally nilpotent and if all of its с-nilpotent subgroups are of finite rank, then G is of finite rank. If G is a non-periodic locally nilpotent group, these results, in general, are not valid.