Category:Symmetric Groups of Same Order are Isomorphic

This category contains pages concerning Symmetric Groups of Same Order are Isomorphic:

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $T_1$ and $T_2$ be sets whose cardinality $\card {T_1}$ and $\card {T_2}$ are both $n$.

Let $\struct {\map \Gamma {T_1}, \circ}$ and $\struct {\map \Gamma {T_2}, \circ}$ be the symmetric group on $S$ and $T$ respectively.

Then $\struct {\map \Gamma {T_1}, \circ}$ and $\struct {\map \Gamma {T_2}, \circ}$ are isomorphic.