A note on central automorphisms of groups
A characterization of central automorphisms of groups is given. As an application, we obtain a new proof of the centrality of power automorphisms.
A Note On Generalization Of Some Undecidability Results In Group Theory
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).
A note on groups with hamiltonian quotients
A note on groups with torsion-free abelianization and trivial multiplicator.
A note on -endomorphisms of two-generated metabelian groups
A note on infinite -groups
Let be a group. If every nontrivial subgroup of has a proper supplement, then is called an -group. We study some properties of -groups. For instance, it is shown that a nilpotent group is an -group if and only if is a subdirect product of cyclic groups of prime orders. We prove that if is an -group which satisfies the descending chain condition on subgroups, then is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group is an -group....
A note on locally graded groups
A note on supersoluble maximal subgroup and theta-pairs.
A θ-pair for a maximal subgroup M of a group G is a pair (A, B) of subgroups such that B is a maximal G-invariant subgroup of A with B but not A contained in M. θ-pairs are considered here in some groups having supersoluble maximal subgroups.
A note on systems of ideals
A note on the Jordan-Hölder theorem
A note on the Lawrence-Krammer-Bigelow representation.
A note on the rank of self-dual polyhedra
A note on torsion-by-nilpotent groups
A numerical invariant for finitely generated groups via actions on graphs.
A proof of Ph. Hall's theorem on dimension subgroups
A property equivalent to commutativity for infinite groups
A property equivalent to permutability for groups
A property of Generalized McLain groups