Almost abelian numbers

TL;DR

This paper introduces almost -numbers, surveys related results, and proves that almost abelian and almost nilpotent numbers are equivalent concepts.

Contribution

It defines almost -numbers and establishes the equivalence between almost abelian and almost nilpotent numbers.

Findings

Almost abelian and almost nilpotent numbers are equivalent.

Provides characterizations for these classes of numbers.

Surveys existing literature on almost cyclic numbers.

Abstract

In this article we introduce the concept of almost $\mathcal{P}$-numbers. We survey the existing results in literature for almost cyclic numbers and give characterizations for almost abelian and almost nilpotent numbers proving these two are equivalent.