Geodesic
The groups whose cyclic subgroups are either ascendant or almost self-normalizing
Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 111-127

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The main result of this paper shows a description of locally finite groups, whose cyclic subgroups are either almost self-normalizing or ascendant. Also, we obtained some natural corollaries of the above situation.
Keywords: locally finite group, self-normalizing subgroup, ascendant subgroup, subnormal subgroup, Gruenberg radical, Baer radical. 
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Leonid A. Kurdachenko; Aleksandr A. Pypka; Nikolaj N. Semko. The groups whose cyclic subgroups are either ascendant or almost self-normalizing. Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 111-127. http://geodesic.mathdoc.fr/item/ADM_2016_21_1_a7/