Seminormal subgroup
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In mathematics, in the field of group theory, a subgroup [math]\displaystyle{ A }[/math] of a group [math]\displaystyle{ G }[/math] is termed seminormal if there is a subgroup [math]\displaystyle{ B }[/math] such that [math]\displaystyle{ AB = G }[/math], and for any proper subgroup [math]\displaystyle{ C }[/math] of [math]\displaystyle{ B }[/math], [math]\displaystyle{ AC }[/math] is a proper subgroup of [math]\displaystyle{ G }[/math]. 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.
References
- ↑ Su, Xiang Ying (1988), "Seminormal subgroups of finite groups", Journal of Mathematics 8 (1): 5–10.
- ↑ Foguel, Tuval (1994), "On seminormal subgroups", Journal of Algebra 165 (3): 633–635, doi:10.1006/jabr.1994.1135. Foguel writes: "Su introduces the concept of seminormal subgroups and using this tool he gives four sufficient conditions for supersolvability."
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