Among other things, we prove that the group of automorphisms fixing every normal subgroup of a (nilpotent of class c)-by-abelian group is (nilpotent of class ≤ c)-by-metabelian. In particular, the group of automorphisms fixing every normal subgroup of a metabelian group is soluble of derived length at most 3. An example shows that this bound cannot be improved.

‎we characterize those groups $g$ and vector spaces $v$ such that $v$ is a faithful irreducible $g$-module and such that each $v$ in $v$ is centralized by a $g$-conjugate of a fixed non-identity element of the fitting subgroup $f(g)$ of $g$‎. ‎we also determine those $v$ and $g$ for which $v$ is a faithful quasi-primitive $g$-module and $f(g)$ has no regular orbit‎. ‎we do use these to show in ...

In this article we define a new form of unipotence in groups finite Morley rank which extends Burdges to any characteristic. particular, show that every connected solvable group $G$ has definable subgroup $H$ whose derived $H'$ is good unipotent rank.

1. Let G be a connected locally compact group and let G' denote the closure of the commutator subgroup of G. G' is called the derived subgroup of G. Consider the derived series of G, that is, the sequence of subgroups Go, Gi, ■ ■ ■ , Gn, ■ ■ ■ where G0 = G and Gn+i = G'nEach Gn is connected and this sequence becomes stationary at some finite stage,2 that is, for some n, Gn = Gn+i. We define Gn ...

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

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in this paper we illustrate recent results about factorizations of finite groups into conjugate subgroups. the illustrated results are joint works with john cannon, dan levy, attila mar'oti and iulian i. simion.

we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.‎