We characterize the solvable groups without infinite properly ascending chains of non-BFC subgroups and prove that a non-BFC group with a descending chain whose factors are finite or abelian is a Cernikov group or has an infinite properly descending chain of non-BFC subgroups.
@article{urn:eudml:doc:41407, title = {Solvable groups with many BFC-subgroups.}, journal = {Publicacions Matem\`atiques}, volume = {44}, year = {2000}, pages = {491-501}, mrnumber = {MR1800820}, zbl = {0978.20016}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41407} }
Artemovych, O. D. Solvable groups with many BFC-subgroups.. Publicacions Matemàtiques, Tome 44 (2000) pp. 491-501. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41407/