Normal complements in finite solvable groups

Maximal complements in finite groups

Let G be a finite group with a non-abelian minimal normal subgroup N which is a direct product of the simple group X. The maximal subgroups of G which complement N and their conjugacy classes are parametrised in terms of certain homomorphisms taking values in AutX and satisfying particular conditions.

Fundamental Groups of Complements of Branch Curves as Solvable Groups

In this paper we show that fundamental groups of complements of curves are “small” in the sense that they are “almost solvable”. Thus we can start to compute π2 as a module over π1 in order to produce new invariants of surfaces that might distinguish different components of a moduli space. 0. Applications of the calculations of fundamental groups to algebraic surfaces. Our study of fundamental ...

finite bci-groups are solvable

‎let $s$ be a subset of a finite group $g$‎. ‎the bi-cayley graph ${rm bcay}(g,s)$ of $g$ with respect to $s$ is an undirected graph with vertex set $gtimes{1,2}$ and edge set ${{(x,1),(sx,2)}mid xin g‎, ‎ sin s}$‎. ‎a bi-cayley graph ${rm bcay}(g,s)$ is called a bci-graph if for any bi-cayley graph ${rm bcay}(g,t)$‎, ‎whenever ${rm bcay}(g,s)cong {rm bcay}(g,t)$ we have $t=gs^alpha$ for some $...

Classifying fuzzy normal subgroups of finite groups

In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

Engel-like Identities Characterizing Finite Solvable Groups