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 descendant if there is a descending series starting from the subgroup and ending at the group, such that every term in the series is a
normal subgroup of its predecessor.
The series may be infinite. If the series is finite, then the subgroup is
subnormal.
See also
*
Ascendant subgroup
In mathematics, in the field of group theory, 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 id ...
References
*
Subgroup properties
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