On the isomorphism problem for certain $p$-groups

TL;DR

This paper investigates the isomorphism problem for nine infinite families of finite p-groups, providing solutions for when their defining parameters are altered, thus advancing understanding of their structural classification.

Contribution

It solves the isomorphism problem for nine specific families of p-groups under parameter modifications, a previously unresolved classification challenge.

Findings

Complete classification of isomorphisms for the nine families

Identification of parameter conditions affecting group isomorphism

Extension of known results in p-group theory

Abstract

We consider 9 infinite families of finite $p$-groups, for $p$ a prime, and we settle the isomorphism problem that arises when the parameters that define these groups are modified.