Further variations on the theme of FC-groups

摘要

Groups that are FC, or more generally satisfy any of the weakenings of the FC-condition considered in de Giovanni (Serdica Math. J. 28:241–254, 2002) and Robinson et al. (J. Algebra 326:218–226, 2011), have local systems consisting of normal finite-by-nilpotent subgroups. Apart from generalizing results from de Giovanni (Serdica Math. J. 28:241–254, 2002) and Robinson et al. (J. Algebra 326:218–226, 2011) to the more general context of locally (normal and finite-by-nilpotent) groups, we partially settle an open problem raised in Robinson et al. (J. Algebra 326:218–226, 2011) concerning the isomorphism of maximal p-subgroups, but in this more general setting of locally (normal and finite-by-nilpotent) groups.