On a question of Deaconescu about automorphisms. - III
On groups with many nearly maximal subgroups
A subgroup of a group is nearly maximal if the index is infinite but every subgroup of properly containing has finite index, and the group is called nearly if all its subgroups of infinite index are intersections of nearly maximal subgroups. It is proved that an infinite (generalized) soluble group is nearly if and only if it is either cyclic or dihedral.
On maximal subgroups of minimax groups
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 maximal subgroups of the general linear group over the field of rational functions.
On nonnilpotent groups in which every two 3-maximal subgroups are permutable.
On -quasinormal and -normal subgroups of a finite group
Let be a saturated formation containing the class of supersolvable groups and let be a finite group. The following theorems are presented: (1) if and only if there is a normal subgroup such that and every maximal subgroup of all Sylow subgroups of is either -normal or -quasinormally embedded in . (2) if and only if there is a normal subgroup such that and every maximal subgroup of all Sylow subgroups of , the generalized Fitting subgroup of , is either -normal or -quasinormally...
On some Bruhat decomposition and the structure of the Hecke rings of -adic Chevalley groups
On some metabelian 2-groups and applications I
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 , where is the second Hilbert 2-class field of k.
On some questions concerning permutable subgroups of finitely generated groups and projectivities of perfect groups
On subsemigroup lattices of aperiodic groups.
On the Burnside problem for groups of even exponent.
On the intersection of maximal non-supersoluble subgroups in a finite group
Gli autori studiano il sottogruppo intersezione dei sottogruppi massimali e non supersolubili di un gruppo finito e le relazioni tra la struttura di e quella di .
On the Maximality of the Orthogonal Groups in the Symplectic Groups in Characteristic Two.
On the number of maximal theta pairs in a finite group
On the -supersolubility of a finite group with a -supplemented Sylow -subgroup.
On the Structure of Locally Compact Topological Groups.
On the Structure of the Normal Subgroups of a Group: Nilpotency.
On the structure of the normal subgroups of a group : supersolubility