Search
Menu
Home
Sources
About
Contacts
Norm (group)
In
mathematics
, in
the field
of
group theory
, the
norm
of a
group
is the
intersection
of the normalizers of all its
subgroups
. This is also termed the
Baer
norm
, after
Reinhold Baer
.
The following
facts
are
true
for the Baer norm:
It is a
characteristic subgroup
.
It contains the
center
of the group.
It is contained
inside
the second term of the
upper central series
.
It is a
Dedekind group
, so is either abelian or has a
direct
factor
isomorphic to the
quaternion group
.
If it contains an
element of
infinite
order, then it is
equal to
the center of the group.
