Abstract
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.
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References
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Wehrfritz, B. Further variations on the theme of FC-groups. Ricerche mat. 61, 103–115 (2012). https://doi.org/10.1007/s11587-011-0116-y
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DOI: https://doi.org/10.1007/s11587-011-0116-y