Groups with at most 13 nonpower subgroups

TL;DR

This paper extends the classification of groups based on the number of nonpower subgroups, specifically focusing on groups with up to 13 such subgroups, building on previous work with at most 9.

Contribution

It advances the classification of groups with a limited number of nonpower subgroups from 9 to 13, providing new insights into their structure.

Findings

Extended classification to groups with up to 13 nonpower subgroups

Identified structural properties of groups with few nonpower subgroups

Built upon previous classifications for groups with at most 9 nonpower subgroups

Abstract

For a group G and positive interger m, Gm denotes the subgroup generated by the elements gm where g runs through G. The subgroups not of the form Gm are called nonpower subgroups. We extend the classification of groups with few nonpower subgroups from groups with at most 9 nonpower subgroups to groups with at most 13 nonpower subgroups.