Seminormal subgroup

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In mathematics, in the field of group theory, a subgroup of a group is termed seminormal if there is a subgroup such that , and for any proper subgroup of , is a proper subgroup of .

This definition of seminormal subgroups is due to Xiang Ying Su.[1][2]

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


  1. ^ Su, Xiang Ying (1988), "Seminormal subgroups of finite groups", Journal of Mathematics, 8 (1): 5–10, MR 0963371.
  2. ^ Foguel, Tuval (1994), "On seminormal subgroups", Journal of Algebra, 165 (3): 633–635, doi:10.1006/jabr.1994.1135, MR 1275925. Foguel writes: "Su introduces the concept of seminormal subgroups and using this tool he gives four sufficient conditions for supersolvability."