Some examples of semigroup algebras of finite representation type

The semigroup algebras over a field $K$ of the semigroups $T_n$ of all permutations of a set of $n$ elements are considered. It is proved: if $n\leq3$ and $(n!)^{-1}\in K$ then the algebra $KT_n$ has a finite representation type. Also the finiteness of the representation type of the semigroup algebra $KS$ is established, where $S$ is the sub-semigroup of $T_n$ ($n$ is arbitrary) such that $S=J_n\cup G$ where $J_n=\{x\in T_n|\operatorname{rank}x=1\}$, while $G$ is a doubly transitive subgroup of the symmetric group $S_n$, the order of $G$ being invertible in $K$.