The construction of finite solvable groups revisited

TL;DR

This paper introduces a new systematic approach and practical algorithm for constructing finite solvable groups up to isomorphism, with implementation and applications demonstrated using GAP.

Contribution

It presents a novel method and algorithm for the systematic construction of finite solvable groups, including a GAP implementation.

Findings

Successful implementation of the algorithm in GAP

Construction of various finite solvable groups demonstrated

Potential applications in group theory research

Abstract

We describe a new approach towards the systematic construction of finite groups up to isomorphism. This approach yields a practical algorithm for the construction of finite solvable groups up to isomorphism. We report on a GAP implementation of this method for finite solvable groups and exhibit some sample applications.