In an infinite group G contains a finite subgroup H, how to calculate the index of H in G for example the braid groups over the 2 sphere?

the braid group over the 2 sphere Bn(S2) is infinite if n greather than 3 but this group contain elements of finite order so this element generate a finite cyclic subgroup H in Bn(S2) my question...

02 February 2016 4,001 12 View