Clones determined by alternating monoids

In the symmetric semigroup $\mathcal T_k$ of all mappings from the set $E_k$ into $E_k$, $k\geq3$, we consider alternating monoids, that is, monoids which contain all even permutations on $E_k$. For each monoid $T\in\mathcal T_k$, we define the set of all functions of $P_k$ which preserve graphs of all permutations of $T$ (the clone determined by the monoid $T$). We describe all clones determined by alternating monoids.
The research was supported by the Russian Foundation for Basic Research, grant 00–01–00351.