Terminology: reversing the order of the generators.

Question

Let $H=\langle Y\mid S\rangle$ be a finite group. Then, for all $h\in H$, we can write

$$h=y_1^{\eta_1}\dots y_m^{\eta_m}$$

for some finite $m\in\Bbb N$ and finite $\eta_i\in\Bbb Z$, for $y_i\in Y$.

Is there a name for $h^{\leftarrow}$ such that $$h^{\leftarrow}=y_m^{\eta_m}\dots y_1^{\eta_1};$$ that is, the product of $y_i^{\eta_i}$, where $i$ runs through $\{1,\dots, m\}$ in descending (rather than ascending) order?

I do realise that this definition depends on the choice of $Y$.

Answer 1

Sometimes this is called "reversal" of $h$, see for example in the article Trace polynomials in special linear groups by Southcott on page 408. He denotes it by ${\rm rev}(h)$.