Contranormal subgroup
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In mathematics, in the field of group theory, a contranormal subgroup is a subgroup whose normal closure in the group is the whole group.[1] 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
- Rose, John S. (1968), "Nilpotent Subgroups of Finite Soluble Groups", Math. Z. 106 (2): 97–112, doi:10.1007/BF01110717, http://resolver.sub.uni-goettingen.de/purl?GDZPPN002402750
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