Some Remarks on Groups with Action on Itself

TL;DR

This paper explores the properties of small groups with self-action by implementing GAP functions and analyzing groups of order less than 32 to understand their basic characteristics.

Contribution

It introduces GAP functions for groups with action on itself and provides an investigation of small such groups, highlighting their fundamental properties.

Findings

Analysis of groups with action on itself of order less than 32

Implementation of GAP functions for these groups

Identification of basic properties of small groups with self-action

Abstract

We implement GAP functions about groups with action on itself and investigate some basic properties of small groups with action on itself of order $<32$.