Let H < PSL 2 ( Z ) be a finite index normal subgroup which is contained in principal congruence subgroup, and let Φ ≠ denote term of the lower central series or derived H. In this paper, we prove that commensurator R discrete. We thus obtain natural family thin subgroups whose commensurators are discrete, establishing some cases conjecture Shalom.

abstract background: in this study we aimed to examine the discrimination and calibration of a severity characterization of trauma (ascot) in our setting to determine whether its usage is appropriate to predict outcome of our trauma patients. methods: this study was conducted in three hospitals. all patients admitted in studied hospitals were divided randomly into two equal subgroups. in each g...

The aim of this paper is to give a new elementary proof for our previous theorem, in which the Lie derived length and the strong Lie derived length of group algebras are determined in the case when the derived subgroup of the basic group is cyclic of odd order.

a celebrated result of i. schur asserts that the derived subgroup of a group is finite provided the group modulo its center is finite, a result that has been the source of many investigations within the theory of groups. in this paper we exhibit a similar result to schur's theorem for vector spaces, acted upon by certain groups. the proof of this analogous result depends on the characteristic o...

Let K be field of characteristic 2 and let G be a finite nonabelian 2-group with the cyclic derived subgroup G′, and there exists a central element z of order 2 in Z(G)\G′. We prove that the unit group of the group algebra KG possesses a section isomorphic to the wreath product of a group of order 2 with the derived subgroup of the group G, giving for such groups a positive answer to the questi...

Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...