Geodesic
On groups with many nearly maximal subgroups
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 1, pp. 19-23

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A subgroup \( M \) of a group \( G \) is nearly maximal if the index \( |G : M | \) is infinite but every subgroup of \( G \) properly containing \( M \) has finite index, and the group \( G \) is called nearly \( IM \) if all its subgroups of infinite index are intersections of nearly maximal subgroups. It is proved that an infinite (generalized) soluble group is nearly \( IM \) if and only if it is either cyclic or dihedral. 
Franciosi, Silvana; de Giovanni, Francesco. On groups with many nearly maximal subgroups. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 1, pp. 19-23. http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_1_a1/
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     author = {Franciosi, Silvana and de Giovanni, Francesco},
     title = {On groups with many nearly maximal subgroups},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {19--23},
     year = {1998},
     volume = {Ser. 9, 9},
     number = {1},
     zbl = {0924.20021},
     mrnumber = {MR1669256},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_1_a1/}
}
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