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Valuation Group

Let $(K, \vert\cdot\vert)$ be a valuated field. The valuation group $G$ is defined to be the set

G = \{\vert x\vert: x \in K, x \not= 0\},

with the group operation being multiplication. It is a Subgroup of the Positive Real Numbers, under multiplication.

© 1996-9 Eric W. Weisstein