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For the Baer norm (intersection of normalizers), see
Norm (group).
In
mathematics, specifically
abstract algebra, if
is an (
abelian)
group with identity element
then
is said to be a norm on
if:
-
Positive definiteness:
,
-
Subadditivity:
,
- Inversion (Symmetry):
.
[1]
An alternative, stronger definition of a norm on
requires
,
,
.
[2]
The norm
is discrete if there is some
real number
such that
whenever
.
Free abelian groups
An abelian group is a
free abelian group
if and only if it has a discrete norm.
[2]
References