I want clarification on a question from Gallian's book contemporary abstract algebra, 8th edition, number 62 of section 6. The statement to be proven is:
Let $G$ be a finite group. Then in disjoint cycles form of the right regular representation $T_g (x) = xg$ of $G$, each cycle has length $|g|$.
I'm not quite sure what I'm supposed to show here. A restatement might be all I need to start trying things. I don't really know what is meant by right regular representation. They don't really say anything about what $x$ and $g$ are here. I'm not looking for how to prove the statement, just what the statement means.