The distinguishing number of groups based on the distinguishing number of subgroups

Saeid Alikhani, Samaneh Soltani

Let $\Gamma$ be a group acting on a set $X$. The distinguishing number for this action of $\Gamma$ on $X$, denoted by $D_{\Gamma }(X)$, is the smallest natural number $k$ such that the elements of $…