Arithmetic graphs of finite groups

TL;DR

This paper introduces arithmetic graph functions for finite groups, linking group divisors to directed graphs, and explores how these graphs can characterize classes of groups, especially hereditary saturated formations.

Contribution

It defines arithmetic graph functions for groups and investigates their use in recognizing group classes, advancing understanding of group classification via graph invariants.

Findings

Arithmetic graphs are associated with group divisors.

Recognition of group classes via arithmetic graphs is formulated.

Results are provided for specific arithmetic graph functions.

Abstract

In this paper we introduced an arithmetic graph function which associates with every group G the directed graph whose vertices corresponds to the divisors of |G|. With the help of such functions we introduced arithmetic graphs of classes of groups, in particular of hereditary saturated formations. We formulated the problem of the recognition of classes of groups by arithmetic graph functions and investigated this problem for some arithmetic graph functions.