Homotopy nilpotency in p-compact groups

TL;DR

This paper investigates the homotopy nilpotency class of p-compact groups, specifically those with the homotopy type of p-completed products of spheres, advancing understanding in homotopy theory.

Contribution

It determines the homotopy nilpotency class for a class of p-compact groups, linking algebraic properties with topological structures.

Findings

Homotopy nilpotency class of p-compact groups with sphere product type identified

Provides new insights into the structure of p-compact groups

Advances the classification of p-compact groups based on homotopy properties

Abstract

A p-compact group is a mod p homotopy theoretical analogue of a compact Lie group. It is determined the homotopy nilpotency class of a p-compact group having the homotopy type of the $p$-completion of the direct product of spheres.