In
mathematics, in the field of
group theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups.
The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ...
, a
subgroup
In group theory, a branch of mathematics, given a group ''G'' under a binary operation ∗, a subset ''H'' of ''G'' is called a subgroup of ''G'' if ''H'' also forms a group under the operation ∗. More precisely, ''H'' is a subgroup ...
of a
group
A group is a number of persons or things that are located, gathered, or classed together.
Groups of people
* Cultural group, a group whose members share the same cultural identity
* Ethnic group, a group whose members share the same ethnic ide ...
is said to be polynormal if its
closure under conjugation by any element of the group can also be achieved via closure by conjugation by some element in the subgroup generated.
In symbols, a subgroup
of a group
is called polynormal if for any
the subgroup
is the same as
.
Here are the relationships with other subgroup properties:
* Every weakly
pronormal subgroup is polynormal.
* Every
paranormal subgroup is polynormal.
Subgroup properties
{{Abstract-algebra-stub