Given a prime number we consider
, which is usually called the Tate field,
the topological completion of the
algebraic closure of the field of -adic numbers. We introduce and study a class of modules
associated with factor groups of profinite groups, especially of those which are the Galois groups
of the normal closure of algebraic infinite extensions. In particular, we show that the module
associated with a Galois orbit of an arbitrary element of
is a factor of the Iwasawa algebra
of a normal element of
by an ideal which can be described.

Key words and phrases: Galois orbits, Iwasawa algebra, local fields, distributions.

2010 Mathematics Subject Classification: 11S99.

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