On the structure of some infinite dimensional linear groups

Abstract

If G is a group and if the upper hypercenter, Z, of G is such that G/Z is nite then a recent theorem shows that G contains a nite normal subgroup L such that G/L is hypercentral. The purpose of the current paper is to obtain a version of this result for subgroups G of GL(F, A), when A is an in nite dimensional F-vector space.

On some topics in the theory of infinite dimensional linear groups

“…A generalization of the result of P. Hall was obtained in [18] where it was proved that a group G has a finite normal subgroup K such that G/K is hypercentral if and only if the upper hypercenter of G has finite index. Linear analogues of this result also hold and we now give these results which were obtained in [14].…”

On some properties of the upper central series in Leibniz algebras

“…This result also had further extensions, see for example [4], [5]. The above mentioned fundamental results and other results of this topic have analogs in other algebraic structures, see for example [12].…”