Some new examples of simple $p$-local compact groups

TL;DR

This paper introduces new examples of simple p-local compact groups for all odd primes and develops tools to analyze their properties, including saturation and non-realizability as classical groups.

Contribution

It provides the first known examples of simple p-local compact groups for all odd primes and offers methods to verify their structural properties.

Findings

New examples of simple p-local compact groups for all odd primes.

Tools for proving saturation and simpleness.

Results showing non-realizability as p-compact or Lie groups.

Abstract

In this paper we present new examples of simple $p$-local compact groups for all odd primes. We also develop the necessary tools to show saturation, simpleness and the non-realizability as $p$-compact groups or compact Lie groups, which can be applied in a more general framework.