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Contranormal subgroup
In
mathematics
, in
the field
of
group theory
, a
contranormal
subgroup
is a subgroup whose
normal closure
in the group is the
whole
group.
Clearly
, a contranormal subgroup can be
normal
only if it is the whole group.
Some facts:
Every subgroup of a
finite group
is a contranormal subgroup of a
subnormal subgroup
.
In general
, every subgroup of a group is a contranormal subgroup of a
descendant subgroup
.
Every
abnormal subgroup
is contranormal.
