| Abstract: | Suppose G is a group and D a subgroup. A system, of intermediate subgroups G
and their normalizers is called a fan for D if for each intermediate sub group H (D  HG) there exists a unique index 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 G
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.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 94, pp. 5–12, 1979. |
