Elements of the group R, which satisfy g2 D i (where i is the identity element of R), are sometimes.

Elements of the group R, which satisfy g2 D i (where i is
the identity element of R), are sometimes called ‘involutions’. Do these
involutions form a subgroup of R?

Demonstrate that, if G is an Abelian group and H is an
arbitrary subgroup, then the left cosets, the right cosets and the double
cosets are one and the same set of sets.