Infinite groups almost all of whose elements are prime powers

TL;DR

This paper constructs specific infinite countable groups for each prime p, where only p-1 elements are not pth powers, revealing new structures in the theory of infinite groups.

Contribution

It introduces a method to build infinite groups with a controlled number of elements that are not pth powers for any prime p.

Findings

For each prime p, constructed groups have exactly p-1 elements not pth powers.

The groups are infinite and countable, with a precise element power structure.

Provides new examples in the study of infinite group element properties.

Abstract

For every prime $p$, we construct an infinite countable group that contains precisely $p-1$ elements which are not $p$th powers.