Limits over orbit categories of locally finite groups

TL;DR

This paper corrects previous work and explores derived functors of inverse limits over orbit categories of locally finite groups, showing reductions to finite cases and generalizing spectral sequences.

Contribution

It provides new methods to analyze higher limits over orbit categories of infinite locally finite groups, extending existing spectral sequence techniques.

Findings

Reduces complex limits over infinite groups to finite group cases

Generalizes Lyndon-Hochschild-Serre spectral sequence for higher limits

Clarifies errors in previous literature

Abstract

We correct an error in the paper [BLO3], and take the opportunity to examine in more detail the derived functors of inverse limits over orbit categories of (infinite) locally finite groups. The main results show how to reduce this in many cases to limits over orbit categories of finite groups, but we also look at generalizations of the Lyndon-Hochschild-Serre spectral sequence for higher limits over orbit categories for an extension of locally finite groups.