Let $G$ be a group of order 2n. Suppose half of the element of G are of order 2 and the other half form a subgroup $H$ of order n . Prove that $H$ is of odd order and is an abelian subgroup of $G$
What could i see is..
if we prove that order of every element of $H$ is odd , then order of $H$ is odd . Also i am unable to use the fact that half of the element of $G$ are of order 2.
Please help me to clear this.