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 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.
A short proof of a theorem of Brodskii.
A short proof, using graphs and groupoids, is given of Brodskii’s theorem that torsion-free one-relator groups are locally indicable.