In mathematics, 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
- Rose 1968, p. 97
Bibliography
- Rose, John S. (1968), "Nilpotent Subgroups of Finite Soluble Groups", Math. Z., 106 (2): 97–112, doi:10.1007/BF01110717, S2CID 122382903
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