We introduce and study an analog of p-groups in general scheme theory. It is proved that a scheme C is a p-scheme if and only if so is each homogeneous component of C. Moreover, the automorphism group of a p-scheme is a p-group, and the 2-orbit scheme of a permutation group G is a p-scheme if and only if G is a p-group. Both of these assertions follow from the fact that the class of p-schemes is closed with respect to extensions. Bibliography: 9 titles.
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