On a question of Deaconescu about automorphisms
On a question of Deaconescu about automorphisms. - II
On almost normal subgroups of supersoluble groups
Un sottogruppo di un gruppo si dice «almost normal» se ha soltanto un numero finito di coniugati in , e ovviamente l'insieme costituito dai sottogruppi almost normal di è un sottoreticolo del reticolo di tutti i sottogruppi di . In questo articolo vengono studiati gli isomorfismi tra reticoli di sottogruppi almost normal, provando in particolare che se è un gruppo supersolubile e è un gruppo FC-risolubile tale che i reticoli e sono isomorfi, allora anche è supersolubile, e...
On automorphisms fixing subnormal subgroups of soluble groups
The group of all automorphisms leaving invariant every subnormal subgroup of the group is studied. In particular it is proved that is metabelian if is soluble, and that is either finite or abelian if is polycyclic.
On complete nilpotent groups.
On Finitely Generated Soluble Linear Groups.
On group automorphisms fixing subnormal subgroups setwise
In questo lavoro si studiano i gruppi , , degli automorfismi di un gruppo che fissano — come insiemi — tutti i sottogruppi di che risultano essere rispettivamente subnormali, subnormali di difetto al più , oppure che sono compresi tra un sottogruppo caratteristico ed il suo derivato. Si danno condizioni sufficienti affinché tali gruppi siano parasolubili di para-altezza al più 2 o 3. Si generalizzano così risultati da [4], [7], [8], [10].
On Groups whose Contranormal Subgroups are Normally Complemented
2000 Mathematics Subject Classification: 20F16, 20E15.Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.
On inert subgroups of a group
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 metabelian groups with derived quotient an elementary Abelian 2-group of rank 3.
On non-supersoluble and non-polycyclic normal subgroups
On normal verbal embeddings of some classes of groups.
On one-relator soluble groups.
On products of soluble groups of finite rank.
On residually finite groups and their generalizations
The paper is concerned with the class of groups satisfying the finite embedding (FE) property. This is a generalization of residually finite groups. In [2] it was asked whether there exist FE-groups which are not residually finite. Here we present such examples. To do this, we construct a family of three-generator soluble FE-groups with torsion-free abelian factors. We study necessary and sufficient conditions for groups from this class to be residually finite. This answers the questions asked in...
On soluble groups in which centralizers are finitely generated
On soluble groups of automorphisms of nonorientable Klein surfaces
We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.
On soluble groups of module automorphisms of finite rank
Let be a commutative ring, an -module and a group of -automorphisms of , usually with some sort of rank restriction on . We study the transfer of hypotheses between and such as Noetherian or having finite composition length. In this we extend recent work of Dixon, Kurdachenko and Otal and of Kurdachenko, Subbotin and Chupordia. For example, suppose is -Noetherian. If has finite rank, then also is -Noetherian. Further, if is -Noetherian and if only certain abelian sections...
On solvable groups of exponent 4.