A remark on the intersection of the conjugates of the base of quasi-HNN groups.
A remark on the irreducible characters and fake degrees of finite real reflection groups.
A Root System for the Lyons Group.
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.
A Short Proof of a Theorem of Burns.
A simple proof of Vinogradov’s theorem on the orderability of the free product of -groups
A spelling theorem for staggered generalized 2-complexes, with applications.
A splitting theorem for linear polycyclic groups.
A Stiefel complex for the orthogonal group of a field.
A Strengthened Freiheitssatz.
A survey on just-non- groups.
A theorem on groups
A topological view of ordered groups
In this expository article we use topological ideas, notably compactness, to establish certain basic properties of orderable groups. Many of the properties we shall discuss are well-known, but I believe some of the proofs are new. These will be used, in turn, to prove some orderability results, including the left-orderability of the group of PL homeomorphisms of a surface with boundary, which are fixed on at least one boundary component.
A very short proof of Forester's rigidity result.
Abelian Extensions of Arbitrary Fields.
Abelian groups with many automorphisms
Abelian ideals of a Borel subalgebra and root systems
Let be a simple Lie algebra and the poset of non-trivial abelian ideals of a fixed Borel subalgebra of . In [8], we constructed a partition parameterised by the long positive roots of and studied the subposets . In this note, we show that this partition is compatible with intersections, relate it to the Kostant-Peterson parameterisation and to the centralisers of abelian ideals. We also prove that the poset of positive roots of is a join-semilattice.
Abelian quasinormal subgroups of groups
Let be any group and let be an abelian quasinormal subgroup of . If is any positive integer, either odd or divisible by , then we prove that the subgroup is also quasinormal in .
Abelian subgroup separability of some one-relator groups.
Abelian subgroups of polycyclic groups.