Tor of a group and counter example

Question

Let $Tor(G) = \{ g \in G | \exists n >0 , g^n = e \}$ of a group $G$ , give an example to $G$ such that $Tor(G)$ is not sub group ?

Easy to prove that $G$ must be non-Abelian and infinite in size, so i thought of matrix but i don't have concrete example

score 3 · Accepted Answer · answered Nov 23 '18 at 10:55

3

Take $\langle x,y\ |\ x^2=y^2=1\rangle$.

answered Nov 23 '18 at 10:55

freakish

score 1 · Answer 2 · answered Nov 23 '18 at 10:59

1

I think the above answer is better, but here's one too. Take the infinite dihedral group. It's generated by reflections (which are torsion elts).

answered Nov 23 '18 at 10:59

Richard Martin

2 Answers2