# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1702.01378