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On groups with many nearly maximal subgroups

Silvana Franciosi, Francesco de Giovanni (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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 I M if all its subgroups of infinite index are intersections of nearly maximal subgroups. It is proved that an infinite (generalized) soluble group is nearly I M if and only if it is either cyclic or dihedral.

On maximal subgroups of minimax groups

Silvana Franciosi, Francesco de Giovanni (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

It is proved that a soluble residually finite minimax group is finite-by-nilpotent if and only if it has only finitely many maximal subgroups which are not normal.

On S -quasinormal and c -normal subgroups of a finite group

Shirong Li, Yangming Li (2008)

Czechoslovak Mathematical Journal

Let be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are presented: (1) G if and only if there is a normal subgroup H such that G / H and every maximal subgroup of all Sylow subgroups of H is either c -normal or S -quasinormally embedded in G . (2) G if and only if there is a normal subgroup H such that G / H and every maximal subgroup of all Sylow subgroups of F * ( H ) , the generalized Fitting subgroup of H , is either c -normal or S -quasinormally...

On some metabelian 2-groups and applications I

Abdelmalek Azizi, Abdelkader Zekhnini, Mohammed Taous (2016)

Colloquium Mathematicae

Let G be some metabelian 2-group satisfying the condition G/G’ ≃ ℤ/2ℤ × ℤ/2ℤ × ℤ/2ℤ. In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem for the 2-ideal classes of some fields k satisfying the condition G a l ( k ( 2 ) / k ) G , where k ( 2 ) is the second Hilbert 2-class field of k.

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