Gruppi ed automorfismi
Groups with dense subnormal subgroups
Groups satisfying the maximal condition on subnormal non-normal subgroups
The structure of (generalized) soluble groups for which the set of all subnormal non-normal subgroups satisfies the maximal condition is described, taking as a model the known theory of groups in which normality is a transitive relation.
Groups with nearly modular subgroup lattice
A subgroup H of a group G is nearly normal if it has finite index in its normal closure . A relevant theorem of B. H. Neumann states that groups in which every subgroup is nearly normal are precisely those with finite commutator subgroup. We shall say that a subgroup H of a group G is nearly modular if H has finite index in a modular element of the lattice of subgroups of G. Thus nearly modular subgroups are the natural lattice-theoretic translation of nearly normal subgroups. In this article we...
A note on groups of infinite rank whose proper subgroups are abelian-by-finite
It is proved that if G is a locally (soluble-by-finite) group of infinite rank in which every proper subgroup of infinite rank contains an abelian subgroup of finite index, then all proper subgroups of G are abelian-by-finite.
A note on groups with few isomorphism classes of subgroups
The structure of infinite groups in which any two (proper) subgroups of the same cardinality are isomorphic is described within the universe of locally graded groups. The corresponding problem for finite groups was considered by R. Armstrong (1958).
Le dimostrazioni di teoremi fondate sull’uso di calcolatori
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 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.
Soluble Groups with Many Černikov Quotients
Si studiano i gruppi risolubili non di Černikov a quozienti propri di Černikov. Nel caso periodico tali gruppi sono tutti e soli i prodotti semidiretti con -gruppo abeliano elementare infinito e gruppo irriducibile di automorfismi di che sia infinito e di Černikov. Nel caso non periodico invece si riconduce tale studio a quello dei moduli a quozienti propri artiniani su un gruppo risolubile finito, e si fornisce una caratterizzazione di tali moduli.
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 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.
Soluble Groups with Many Černikov Quotients
Si studiano i gruppi risolubili non di Černikov a quozienti propri di Černikov. Nel caso periodico tali gruppi sono tutti e soli i prodotti semidiretti con -gruppo abeliano elementare infinito e gruppo irriducibile di automorfismi di che sia infinito e di Černikov. Nel caso non periodico invece si riconduce tale studio a quello dei moduli a quozienti propri artiniani su un gruppo risolubile finito, e si fornisce una caratterizzazione di tali moduli.
On hypercentral subgroups of infinite groups
Groups with finitely many conjugacy classes of non-normal subgroups of infinite rank
It is proved that if a locally soluble group of infinite rank has only finitely many non-trivial conjugacy classes of subgroups of infinite rank, then all its subgroups are normal.
Groups with Normality Conditions for Non-Periodic Subgroups
The structure of (non-periodic) groups in which all non-periodic subgroups have a prescribed property is investigated. Among other choices, we consider properties generalizing normality, like subnormality, permutability and pronormality. Moreover, non-periodic groups whose proper non-periodic subgroups belong to a given group class are studied.
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