Frobenius Kernels of Algebraic Supergroups and Steinberg's Tensor Product Theorem.

For a split quasireductive supergroup G defined over a field, we study structure and representation of Frobenius kernels G r of G and we give a necessary and sufficient condition for G r to be unimodular in terms of the root system of G . We also establish Steinberg's tensor product theorem for G under some natural assumptions. [ABSTRACT FROM AUTHOR]