Maximal subgroups of GL n (D) with finite conjugacy classes

Maximal Subgroups of Subnormal Subgroups ofGLn(D) with Finite Conjugacy Classes

“…Some properties of maximal subgroups of GL n D have been studied in a series of articles, see, e.g., [7][8][9]. Recall that a group G is an FC-group if every element of G has only a finite number of conjugates.…”

“…[17,Example 2.5.10]). Recently, in [7] we showed that any FC maximal subgroup of general skew linear group is abelian. In this article, we state a generalization of this result.…”

On normal subgroups of division rings which are radical over a proper division subring

“…The structure properties of multiplicative subgroups in division rings have been recently studied such as free subgroups ( [4,17]), maximal subgroups ( [2,10,11,15]), subgroups radical over a set ( [1,2,6,16,17,14]), etc. In this paper, we generalize one of Faith's works on division rings which are radical over a proper subring.…”

Nilpotent and polycyclic-by-finite maximal subgroups of skew linear groups

“…In section 2, instead of maximal subgroups of GL n (D), we consider maximal subgroups of subnormal subgroups of GL n (D). The structure of such groups have been investigated in various papers, see, e.g., [6,8,12,14]. As mentioned earlier, if D is an infinite division ring, in [3] it was shown that every nilpotent maximal subgroup of GL n (D) is abelian.…”

“…As mentioned earlier, if D is an infinite division ring, in [3] it was shown that every nilpotent maximal subgroup of GL n (D) is abelian. In [8,Corollary 1], the authors proved that if D is a finite-dimensional division algebra over its center, then every nilpotent maximal subgroup of a subnormal subgroup of GL n (D) is abelian. In [12,Theorem 4], the author showed that (without any condition on dimension) every nilpotent maximal subgroup of a subnormal subgroup of GL n (D) is metabelian.…”