On The $E_\alpha$-Envelopes of Hypercentral Subgroups
Group Theory
2018-09-26 v1
Abstract
The E_{k} envelopes that generalize the double centralizers form a descending chain. In this paper we show that this descending chain stops after finitely many steps for hypercentral subgroups by defining the transfinite forms of some basic descriptions. In particular, we prove that the E_{{\alpha}}- envelopes of hypercentral subgroups are solvable in the class of groups satisfying chain condition on centralizers. These extend previous results on E_{k} envelopes.
Cite
@article{arxiv.1809.09479,
title = {On The $E_\alpha$-Envelopes of Hypercentral Subgroups},
author = {Tuba Çakmak},
journal= {arXiv preprint arXiv:1809.09479},
year = {2018}
}