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
is termed seminormal if there is a subgroup
such that
, and for any proper subgroup
of
,
is a proper subgroup of
.
This definition of seminormal subgroups is due to
Xiang Ying Su.
[. Foguel writes: "Su introduces the concept of seminormal subgroups and using this tool he gives four sufficient conditions for supersolvability."]
Every
normal subgroup is seminormal. For finite groups, every
quasinormal subgroup __NOTOC__
In mathematics, in the field of group theory, a quasinormal subgroup, or permutable subgroup, is a subgroup of a group that commutes (permutes) with every other subgroup with respect to the product of subgroups. The term ''quasinormal su ...
is seminormal.
References
{{reflist
Subgroup properties