I wanted to try and find a bijection between them but I wasn't sure quite how to do it.Suppose that G is a group, H is a subgroup of G, and $\displaystyle g_1,g_2 \in G$. Show that $\displaystyle |g_1 H|=|Hg_2|$.

(Do not assume that G is finite).

Alternatively, is there a way to prove it without using bijections?