# Subsets of symmetric groups Sn

by HeronOde
Tags: groups, subsets, symmetric
I find this convincing. Take the subset of permutations that fix 5: $A := \{\sigma \in S_5 : \sigma(5) = 5 \}$. Then $S_4 \cong A$ and $A \subseteq S_5$. I always take "isomorphic" to mean "the same" in math. We could always relabel the elements of a group with crazy names, but does that really make it a different group? I don't think so.