Seminormal subgroup

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title: "Seminormal subgroup" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["subgroup-properties"] topic_path: "general/subgroup-properties" source: "https://en.wikipedia.org/wiki/Seminormal_subgroup" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

In mathematics, in the field of group theory, a subgroup A of a group G is termed seminormal if there is a subgroup B such that AB = G, and for any proper subgroup C of B, AC is a proper subgroup of G.

This definition of seminormal subgroups is due to Xiang Ying Su.{{citation | last = Su | first = Xiang Ying | issue = 1 | journal = Journal of Mathematics | mr = 963371 | pages = 5–10 | title = Seminormal subgroups of finite groups | volume = 8 | year = 1988}}.{{citation | last = Foguel | first = Tuval | doi = 10.1006/jabr.1994.1135 | issue = 3 | journal = Journal of Algebra | mr = 1275925 | pages = 633–635 | title = On seminormal subgroups | volume = 165 | year = 1994| doi-access = free

Every normal subgroup is seminormal. For finite groups, every quasinormal subgroup is seminormal.

References

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