K-Exit for OD-Characterization of the finite Groups

TL;DR

This paper introduces the K-Exit method, a new approach for OD-Characterization of finite groups, which helps identify prime divisors outside a solvable normal subgroup using specialized tables.

Contribution

The paper presents the K-Exit method and associated tables, providing a novel technique for analyzing prime divisors in the OD-Characterization of finite groups.

Findings

K-Exit method effectively identifies prime divisors outside a normal solvable subgroup.

Tables of K-Exit facilitate the application of the method in group analysis.

The approach enhances understanding of the structure of finite groups.

Abstract

Suppose G is a finite group, and K is a normal solvable subgroup of G. In this paper, we present a powerful method which is called K-Exit. Using this method, we find some members of {\pi}(G) that are not members of {\pi}(K) and for this purpose, we introduce the tables of K-Exit. This method can be applied to OD-Characterization of the finite Groups