The automorphism group of HNN extensions with finite base group
The Automorphism Group of the Free Algebra of Rank Two
The theorem of Czerniakiewicz and Makar-Limanov, that all the automorphisms of a free algebra of rank two are tame is proved here by showing that the group of these automorphisms is the free product of two groups (amalgamating their intersection), the group of all affine automorphisms and the group of all triangular automorphisms. The method consists in finding a bipolar structure. As a consequence every finite subgroup of automorphisms (in characteristic zero) is shown to be conjugate to a group...
The automorphisms of the orthogonal groups ... n (V), n ... 5.
The Baer-Invariant and the Direct Limit.
The Banach-Tarski paradox for the hyperbolic plane (II)
The second author found a gap in the proof of the main theorem in [J. Mycielski, Fund. Math. 132 (1989), 143-149]. Here we fill that gap and add some remarks about the geometry of the hyperbolic plane ℍ².
The based ring of the lowest two-sided cell of an affine Weyl group. II
The Birkhoff-Neumann Embedding of Relatively Free Groups
The categories of free metabelian groups and Lie algebras
The centralizer of a classical group and Bruhat-Tits buildings
Let be a unitary group defined over a non-Archimedean local field of odd residue characteristic and let be the centralizer of a semisimple rational Lie algebra element of We prove that the Bruhat-Tits building of can be affinely and -equivariantly embedded in the Bruhat-Tits building of so that the Moy-Prasad filtrations are preserved. The latter property forces uniqueness in the following way. Let and be maps from to which preserve the Moy–Prasad filtrations. We prove that...
The centre of completed group algebras of pro- groups.
The Characteristic Subgroups of the Baer-Specker Group.
The classification of groups in which every product of four elements can be reordered
The Conjugacy Problem for Free Products of Sixth-Groups with Cyclic Amalgamation.
The conjugacy problem for groups, and Higman embeddings.
The cyclic subgroup separability of certain HNN extensions.
The Dehn functions of and
For at least 3, the Dehn functions of and are exponential. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case was established by Bridson and Vogtmann. Handel and Mosher completed the proof by reducing the lower bound for bigger than 3 to the case . In this note we give a shorter, more direct proof of this last reduction.
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 Embedding of Some Lattices into Lattices of All Subgroups of Free Groups
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 Equations s-1 t-1st=u-1 v-1 uv in a Free Product of Groups.