Invariant subgroups of groups of higher derivations

Abstract:

Let L be a field of characteristic $p > 3$. A subgroup G of the group D of all rank ${p^e}$ higher derivations on L is Galois if G is the group of all d in D having a given subfield in its field of constants. The field of constants of G is denoted as ${L^G}$. The main result states: Let $H \subseteq G$ be Galois subgroups of D. Then H is an invariant subgroup of G if and only if either ${L^H} = {L^G}({L^{{p^r}}})$ for some nonnegative integer r, or ${L^H} \subseteq {L^G}({L^{{p^e}}})$.