Chermak-Delgado Simple Groups

TL;DR

This paper initiates the classification of finite solvable groups with Property A by focusing on Chermak-Delgado simple groups, providing partial classifications under prime restrictions.

Contribution

It introduces the concept of Chermak-Delgado simple groups and advances their classification under specific prime-related restrictions.

Findings

Classification of Chermak-Delgado simple groups under prime restrictions

Reduction of Property A classification to Chermak-Delgado simple groups

Partial results on the structure of solvable Chermak-Delgado simple groups

Abstract

This paper provides the first steps in classifying the finite solvable groups having Property A, which is a property involving abelian normal subgroups. We see that this classification is reduced to classifying the solvable Chermak-Delgado simple groups, which the author defines. The author completes a classification of Chermak-Delgado simple groups under certain restrictions on the primes involved in the group order.