More on the non-solvable graphs and solvabilizers
B Akbari - arXiv preprint arXiv:1806.01012, 2018 - arxiv.org
arXiv preprint arXiv:1806.01012, 2018•arxiv.org
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 …
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 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.
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