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- In mathematics, specifically group theory, an abnormal subgroup is a subgroup H of a group G such that for all x in G, x lies in the subgroup generated by H and H x, where H x denotes the conjugate subgroup xHx−1. Here are some facts relating abnormality to other subgroup properties:
* Every abnormal subgroup is a self-normalizing subgroup, as well as a contranormal subgroup.
* The only normal subgroup that is also abnormal is the whole group.
* Every abnormal subgroup is a , and every weakly abnormal subgroup is a self-normalizing subgroup.
* Every abnormal subgroup is a pronormal subgroup, and hence a , a paranormal subgroup, and a polynormal subgroup. (en)
- Inom gruppteori, en del av matematiken, är en abnormal delgrupp en delgrupp H av en grupp G så att varje x ∈ G befinner sig i delgruppen genererad av H och H x, där Hx betecknar xHx-1. (sv)
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- Inom gruppteori, en del av matematiken, är en abnormal delgrupp en delgrupp H av en grupp G så att varje x ∈ G befinner sig i delgruppen genererad av H och H x, där Hx betecknar xHx-1. (sv)
- In mathematics, specifically group theory, an abnormal subgroup is a subgroup H of a group G such that for all x in G, x lies in the subgroup generated by H and H x, where H x denotes the conjugate subgroup xHx−1. Here are some facts relating abnormality to other subgroup properties: (en)
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- Abnormal subgroup (en)
- Abnormal delgrupp (sv)
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