- Let $G$ be a group and any subset $T$ of $G$ is said to be an independent set in $G$ if $a \notin <T\backslash \{a\}> \; \forall a \in T$
Let $S_n$ be a symmetric group of degree $n.$ Then the size of the independent set is atmost $n-1$.
I know that the transpositions set $\{ (1 2) , (2 3), \cdots ,(n-1 n)\}$ is independent, but how to prove that size of any independent set is atmost $n-1$. Any help would be appreciated. Thank you