In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, 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.
References
Bibliography
*
Subgroup properties
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