A note on influence of subgroup restrictions in finite group structure.
A note on locally graded groups
A note on -solvable and solvable finite 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 continuous extensions of injective morphisms between free groups to relatively fre profinite groups.
Let V be a pseudovariety of finite groups such that free groups are residually V, and let φ: F(A) → F(B) be an injective morphism between finitely generated free groups. We characterize the situations where the continuous extension φ' of φ between the pro-V completions of F(A) and F(B) is also injective. In particular, if V is extension-closed, this is the case if and only if φ(F(A)) and its pro-V closure in F(B) have the same rank. We examine a number of situations where the injectivity of φ' can...
A note on the endomorphisms associated to semi-direct decompositions of a group
A note on the torsion elements in the centralizer of a finite index subgroup.
A note on torsion-by-nilpotent groups
A numerical invariant for finitely generated groups via actions on graphs.
A property equivalent to commutativity for infinite groups
A property of Generalized McLain groups
A property of the variety of 2-Engel groups
A property which ensures that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent
Let be the class of groups satisfying the minimal condition on normal subgroups and let be the class of groups of finite lower central depth, that is groups such that for some positive integer . The main result states that if is a finitely generated hyper-(Abelian-by-finite) group such that for every , there exists a normal subgroup of finite index in satisfying for every , then is finite-by-nilpotent. As a consequence of this result, we prove that a finitely generated hyper-(Abelian-by-finite)...
A radical for free groups
A rank 3 tangent complex of , odd.
A relatively free topological group that is not varietal free
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
A remark about central automorphisms of groups
A remark on the intersection of the conjugates of the base of quasi-HNN groups.
A Residual Property of Certain Free Products.