The amalgamation basis of the category of compact groups.
The Birkhoff-Neumann Embedding of Relatively Free Groups
The Characteristic Subgroups of the Baer-Specker Group.
The conjugacy problem for groups, and Higman embeddings.
The divisible radical of a group
We consider the existence or otherwise of canonical divisible normal subgroups of groups in general. We present more counterexamples than positive results. These counterexamples constitute the substantive part of this paper.
The endocenter and its applications to quasigroup representation theory
A construction is given, in a variety of groups, of a ``functorial center'' called the endocenter. The endocenter facilitates the identification of universal multiplication groups of groups in the variety, addressing the problem of determining when combinatorial multiplication groups are universal.
The -local subgroups of the groups with a generalized finite element of order 2 or 4.
The finite subgroups of maximal arithmetic kleinian groups
Given a maximal arithmetic Kleinian group , we compute its finite subgroups in terms of the arithmetic data associated to by Borel. This has applications to the study of arithmetic hyperbolic 3-manifolds.
The fixed group of an automorphism of a word hyperbolic group is rational.
The Frattini Subgroup of Locally Free Groups.
The homomorphic images of infinite symmetric groups.
The lower garland of subgroup lattices in linear groups.
The maximum order of finite groups of outer automorphisms of free groups.
The periodic groups saturated by finitely many finite simple groups.
The p-period of an infinite group.
For Γ a group of finite virtual cohomological dimension and a prime p, the p-period of Γ is defined to be the least positive integer d such that Farrell cohomology groups Hi(Γ; M) and Hi+d(Γ; M) have naturally isomorphic ZΓ modules M.We generalize a result of Swan on the p-period of a finite p-periodic group to a p-periodic infinite group, i.e., we prove that the p-period of a p-periodic group Γ of finite vcd is 2LCM(|N(〈x〉) / C(〈x〉)|) if the Γ has a finite quotient whose a p-Sylow subgroup is elementary...
The probability that elements of a rank free group generate a rank subgroup.
The structure of subnormal subgroups of symplectic groups over local rings.
The subgroups in the special linear group over a skew field that contain the group of diagonal matrices
The symmetry of intersection numbers in group theory.
The theorem of Borevich for the hyperbolic unitary group over a noncommutative field.