Like in Number Theory, there are many problems in Group Theory which are easy to state to anyone but difficult to solve; one among them is Burnsides problem: *If a group $B\_{m,n}$ is generated by $x\_1,x\_2,\cdots, x\_m$, subject to the relations that $x^n=1$ for all elements $x$ in group, then is $B\_{m,n}$ a finite group?* 

There is interesting history and work on this problem (see, for example, just the *introduction* in the article *Periodic groups of odd exponents: S. I. Adyan*). When I looked some results about this group, immediately, I asked myself, *how can we prove this (these results)*? It turns out that many proofs of some results on group $B\_{m,n}$ are difficult or lengthy. 

Then my question is 

**Question:** What are interesting properties of the group $B\_{m,n}$ which are easy to prove?