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- Subnormal_subgroup abstract "In mathematics, in the field of group theory, a subgroup H of a given group G is a subnormal subgroup of G if there is a finite chain of subgroups of the group, each one normal in the next, beginning at H and ending at G.In notation, is -subnormal in if there are subgroupsof such that is normal in for each .A subnormal subgroup is a subgroup that is -subnormal for some positive integer .Some facts about subnormal subgroups: A 1-subnormal subgroup is a proper normal subgroup (and vice versa). A finitely generated group is nilpotent if and only if each of its subgroups is subnormal. Every quasinormal subgroup, and, more generally, every conjugate permutable subgroup, of a finite group is subnormal. Every pronormal subgroup that is also subnormal, is, in fact, normal. In particular, a Sylow subgroup is subnormal if and only if it is normal. Every 2-subnormal subgroup is a conjugate permutable subgroup.The property of subnormality is transitive, that is, a subnormal subgroup of a subnormalsubgroup is subnormal. In fact, the relation of subnormality can be defined as the transitive closure of the relation of normality.".
- Subnormal_subgroup wikiPageID "2774415".
- Subnormal_subgroup wikiPageRevisionID "544139949".
- Subnormal_subgroup hasPhotoCollection Subnormal_subgroup.
- Subnormal_subgroup subject Category:Subgroup_properties.
- Subnormal_subgroup type Abstraction100002137.
- Subnormal_subgroup type Possession100032613.
- Subnormal_subgroup type Property113244109.
- Subnormal_subgroup type Relation100031921.
- Subnormal_subgroup type SubgroupProperties.
- Subnormal_subgroup comment "In mathematics, in the field of group theory, a subgroup H of a given group G is a subnormal subgroup of G if there is a finite chain of subgroups of the group, each one normal in the next, beginning at H and ending at G.In notation, is -subnormal in if there are subgroupsof such that is normal in for each .A subnormal subgroup is a subgroup that is -subnormal for some positive integer .Some facts about subnormal subgroups: A 1-subnormal subgroup is a proper normal subgroup (and vice versa).".
- Subnormal_subgroup label "Subnormal subgroup".
- Subnormal_subgroup label "Subnormalteiler".
- Subnormal_subgroup sameAs Subnormalteiler.
- Subnormal_subgroup sameAs m.081zrh.
- Subnormal_subgroup sameAs Q2361983.
- Subnormal_subgroup sameAs Q2361983.
- Subnormal_subgroup sameAs Subnormal_subgroup.
- Subnormal_subgroup wasDerivedFrom Subnormal_subgroup?oldid=544139949.
- Subnormal_subgroup isPrimaryTopicOf Subnormal_subgroup.