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Let F be a Henselian field. For a finite extension K of F, the norm factor group [Formula: see text] is computed. As an application, structure of the tame Brauer group of a generalized local field is determined. In particular, we observe that every torsion divisible abelian group is realizable as the tame Brauer group of a generalized local field.

LetDbe a division algebra over its centerFof degreen. Consider the group{\mu_{Z}(D)=\mu_{n}(F)/Z(D^{\prime})}, where{\mu_{n}(F)}is the group of all then-th roots of unity in{F^{*}}, and{Z(D^{\prime})}is the center of the commutator subgroup of the group of units{D^{*}}ofD. It is shown that if{\mu_{Z}(D\otimes_{F}L)\neq 1}for someLcontaining all the primitive{n^{k}}-th roots of unity for all positive integersk, thenDis not split by any cyclic extension ofF. This criterion is employed to prove that some special classes of division algebras are not cyclically split.