We study the relation between Galois group G of a linear difference-differential system and two classes C1 C2 groups that are specializations difference equation differential in this respectively. show almost all C1∪C2 algebraic subgroups G, there is nonempty subset such product any pair from these subsets. These results have potential application to computation system. also give criterion for ...

1. Throughout this paper, K will represent a division ring and L a galois division subring. We are interested in establishing a galois theory for the extension K/L when K/L is locally finite. In order to do this one must identify the galois subrings of K containing L. An example given by Jacobson [4] shows that not every such division subring is galois. However, we obtain that each subring subj...

Recall that the birational anabelian conjecture originating in ideas presented in Grothendieck’s Esquisse d’un Programme [G1] and Letter to Faltings [G2], asserts roughly the following: First, there should exist a group theoretical recipe by which one can recognize the absolute Galois groups GK of finitely generated infinite fields K among all the profinite groups. Second, if G = GK is such an ...

A Galois correspondence for finitely generated field extensions k/h is presented in the case characteristic h = p ^ 0. A field extension k/h is Galois if it is modular and h is separably algebraically closed in k. Galois groups are the direct limit of groups of higher derivations having rank a power of p. Galois groups are characterized in terms of abelian iterative generating sets in a manner ...