Lecture Notes on Bayesian Estimation and Classification
《Lecture Notes on Bayesian Estimation and Classification》 · 第 425 页 · Section 14.2「Torsion Groups and the Burnside Problems」
If $G$ is an $n$-generator group and $G^e=1$, then $G$ is an image of the so-called free Burnside group $B(n,e)=F/F^e$ where $F$ is a free group with $n$ generators; this follows from 2.3.7. In the terminology of 2.2 the group $B(n,e)$ is a free group in the variety of groups of exponent dividing $e$. Thus Burnside's question is whether $B(n,e)$ is finite.