On the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields

In the present paper, we study outer automorphism groups of absolute Galois mixed-characteristic local fields from point view anabelian geometry. Let us recall that it is well-known natural homomorphism group a field to given injective. One main result paper if satisfies certain conditions, then set conjugates image this injective in infinite, which thus implies not normal group. particular, one may conclude impossible establish functorial group-theoretic reconstruction, group, “field-theoretic” subgroup, i.e., homomorphism,