Abstract
Suppose G is a group and D a subgroup. A system , of intermediate subgroups Gα and their normalizers is called a fan for D if for each intermediate sub group H (D ≤ H≤G) there exists a unique indexα such that . If there exists a fan for D, then D is called a fan subgroup of G. Examples of fans and fan subgroups are given. A standard fan is distinguished, for which all of the groups Gα are generated by sets of subgroups conjugate to D. The question of the uniqueness of a fan is discussed. It is proved that any pronormal subgroup is a fan subgroup, and some properties of its fan are noted.
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