Geodesic
Arrangement of subgroups
Zapiski Nauchnykh Seminarov POMI, Rings and modules. Part 2, Tome 94 (1979), pp. 5-12 Cet article a éte moissonné depuis la source Math-Net.Ru

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Suppose $G$ is a group and $D$ a subgroup. A system, of intermediate subgroups $G_\alpha$ and their normalizers is called a fan for $D$ if for each intermediate sub group $H(D\leqslant H\leqslant G)$ 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 $G_\alpha$ 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. 
@article{ZNSL_1979_94_a0,
     author = {Z. I. Borevich},
     title = {Arrangement of subgroups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--12},
     year = {1979},
     volume = {94},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_94_a0/}
}
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Z. I. Borevich. Arrangement of subgroups. Zapiski Nauchnykh Seminarov POMI, Rings and modules. Part 2, Tome 94 (1979), pp. 5-12. http://geodesic.mathdoc.fr/item/ZNSL_1979_94_a0/