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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Invariant subgroups of groups of higher derivations

Authors: James K. Deveney and John N. Mordeson
Journal: Proc. Amer. Math. Soc. 68 (1978), 277-280
MSC: Primary 12F15
MathSciNet review: 0476711
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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}}})$.

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Keywords: Purely inseparable field extension, higher derivation, Galois group of higher derivations
Article copyright: © Copyright 1978 American Mathematical Society