Extensions of abelian by hyper-(cyclic or finite) groups (II)
Extraspecial sections of periodic -groups
-groups and related classes
fc-группы с ограниченными в совокупности порядками элементов периодической части
Group Rings Whose Units Form an FC-Group.
Groups of polynomial growth and expanding maps (with an appendix by Jacques Tits)
Groups saturated by a finite set of groups.
Groups which are isomorphic to their nonabelian subgroups
Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank)
Our main result is that a locally graded group whose proper subgroups are Baer-by-Chernikov is itself Baer-by-Chernikov. We prove also that a locally (soluble-by-finite) group whose proper subgroups are Baer-by-(finite rank) is itself Baer-by-(finite rank) if either it is locally of finite rank but not locally finite or it has no infinite simple images.
Groups whose proper subgroups are locally finite-by-nilpotent
If is a class of groups, then a group is said to be minimal non -group if all its proper subgroups are in the class , but itself is not an -group. The main result of this note is that if is an integer and if is a minimal non (respectively, )-group, then is a finitely generated perfect group which has no non-trivial finite factor and such that is an infinite simple group; where (respectively, , ) denotes the class of nilpotent (respectively, nilpotent of class at most , locally...
Groups with all subgroups subnormal or nilpotent-by-Chernikov
Groups with every subgroup ascendant-by-finite
A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.
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 metamodular subgroup lattice
A group G is called metamodular if for each subgroup H of G either the subgroup lattice 𝔏(H) is modular or H is a modular element of the lattice 𝔏(G). Metamodular groups appear as the natural lattice analogues of groups in which every non-abelian subgroup is normal; these latter groups have been studied by Romalis and Sesekin, and here their results are extended to metamodular groups.
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...
Groups with Restricted Non-Normal Subgroups.
Gruppi con pochi sottogruppi non quasinormali
Homological and Topological Properties of Locally Indicable Groups.
Inert subgroups of uncountable locally finite groups
Let be an uncountable universal locally finite group. We study subgroups such that for every , .
Infinite locally finite groups of type PSL(2,K) or Sz(K) are not minimal under certain conditions.
In classifying certain infinite groups under minimal conditions it is needed to find non-simplicity criteria for the groups under consideration. We obtain some of such criteria as a consequence of the main result of the paper and the classification of finite simple groups.