On the behaviour of the Atiyah Conjecture under taking subgroups and under taking quotients with finite kernel

TL;DR

This paper investigates how the strong Atiyah Conjecture behaves when passing to subgroups and quotients with finite kernel, establishing conditions for the conjecture's stability under these operations.

Contribution

It provides new conditions under which the strong Atiyah Conjecture is preserved when taking subgroups and quotients with finite kernel.

Findings

The strong Atiyah Conjecture carries over to subgroups under certain conditions.

Quotients with finite kernel of groups satisfying the conjecture also satisfy it.

The paper establishes a formal condition linking subgroup properties to the conjecture's validity.

Abstract

We state and prove a condition under which the strong Atiyah Conjecture carries over to subgroups. Moreover, we show that if a group satisfies the (strong) Atiyah Conjecture then any quotient with finite kernel does.