Large groups and their periodic quotients

Abstract

We first give a short group theoretic proof of the following result of Lackenby. If $G$ is a large group, $H$ is a finite index subgroup of $G$ admitting an epimorphism onto a non--cyclic free group, and $g$ is an element of $H$, then the quotient of $G$ by the normal subgroup generated by $g^n$ is large for all but finitely many $n\in \mathbb{Z}$. In the second part of this note we use similar methods to show that for every infinite sequence of primes $(p_1,p_2,...)$, there exists an infinite finitely generated periodic group $Q$ with descending normal series $Q=Q_0⊳Q_1⊳...$, such that ${\bigcap }_i{Q}_i=\{1\}$ and $Q_{i-1}/Q_i$ is either trivial or abelian of exponent $p_i$.

A section about periodic groups is added

References in corpus (1)

• Adding high powered relations to large groups