- Thread starter
- #1

- Mar 10, 2012

- 835

I approached this problem using the permutation representation afforded by $T$ on $G$. Its easy to deduce that the cycle representation of the permutation of $G$ caused by $T$ has $(n-1)/2$ disjoint transpositions, where $n=|G|$. We know, from this, that $n$ is odd but so what? I am not able to exploit the homomorphism property of $T$.