On Codes in (Generalized) Symmetric Groups

In this article, we show that, for the symmetric group $S_n$, the Young subgroup $S_λ$, with $l(λ)\geq 3$, is not a code with respect to a conjugacy class of $S_n$. This provides a partial answer to \cite[Problem 4.1]{FL26}. We then provide a characterization of conjugacy classes $X_i$, such that su