# 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.Template:Fact

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

A good reference for subgroup properties is "A Course in the Theory of Groups" by Derek J.S. Robinson.