turkmath.org

My talk will be about families of special subgroups introduced by Altınel and Baginski in their paper on definable envelopes of nilpotent subgroups of groups satisfying the descending chain condition on centralizers. These subgroups generalize double centralizers and form descending chains. We analyze sufficient conditions such descending chains to stop after finitely many steps. We discuss whether this phenomenon can happen in the class of groups satisfying the chain condition on centralizers. In general, such chains may not stabilize after finitely many steps as I will illustrate by an example.