More on the Non-Solvable Graphs and Solvabilizers
Group Theory
2018-06-05 v1
Abstract
The non-solvable graph of a finite group G is a simple graph whose vertices are the elements of G and there is an edge between x and y if and only if the subgroup generated by x and y is not solvable. The isolated vertices in the non-solvable graph are exactly the elements of the solvable radical of G. Given a finite group G and element x of G, the solvabilizer of x with respect to G is the set of all elements y of G such that the subgroup generated by x and y is solvable. The purpose of this paper is to study some properties of the non-solvable graph and the structure of the solvabilizer of x with respect to G for every element x of G.
Cite
@article{arxiv.1806.01012,
title = {More on the Non-Solvable Graphs and Solvabilizers},
author = {B. Akbari},
journal= {arXiv preprint arXiv:1806.01012},
year = {2018}
}