Frattini theory for classes of finite universal algebras of Mal'tsev varieties

We extend the Frattini theory of formations and Schunck classes of finite groups to some Frattini theory of formations and Schunck classes of finite universal algebras of Malcev varieties. We prove that if $F\neq(1)$ is a nonempty formation (Schunck class) of algebras of a Malcev variety, then its Frattini subformation (Frattini Schunck subclass) $\Phi(F)$ consists of all nongenerators of $F$ moreover, if $M$ is a formation (Schunck class) in $F$ then $\Phi(M)\subseteq\Phi(F)$.