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For a split quasireductive supergroup $G$ defined over a field, we studystructure and representation of Frobenius kernels $G_r$ of $G$ and we give anecessary and sufficient condition for $G_r$ to be unimodular in terms of theroot system of $G$. We also establish Steinberg's tensor product theorem for$G$ under some natural assumptions.

Frobenius kernels of algebraic supergroups and Steinberg's tensor product theorem