Sonlu merkezleyici zincirine sahip grupların cebirsel yapısı

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Thesis Type: Doctorate

Institution Of The Thesis: Ataturk University, Fen Bilimleri Enstitüsü, Matematik Anabilim Dalı, Turkey

Approval Date: 2018

Thesis Language: Turkish

Student: TUBA ÇAKMAK

Principal Supervisor (For Co-Supervisor Theses): Erdal Karaduman

Open Archive Collection: AVESIS Open Access Collection

Abstract:

In this thesis, special classes of subgroups of infinite groups that generalize double centralizers have been analyzed. They are called E_k-envelopes. Sufficient conditions have been analyzed for descending chain of this subgroups to stop after finitely many steps. In this sense, it is proved that the length of the descending chain of E_k-envelopes of a nilpotent subgroup of any group is bounded by the nilpotency class of this subgroup. The stabilization of the descending chain of a hypercentral subgroup of any group is shown by describing the transfinite forms of envelopes and iterated centralizers. Also, the stabilization problem of the chain of E_k-envelopes corresponding to a subgroup of an M_c-group is answered partially positively by topological approaches. In addition to these affirmative conclusions obtained for the stabilization problem of envelopes, a counter example that shows the chain of E_k-envelopes does not have to stabilize has been constructed with all details.