Constructable Solvable Groups.
Co-rank and Betti number of a group
For a finitely generated group, we study the relations between its rank, the maximal rank of its free quotient, called co-rank (inner rank, cut number), and the maximal rank of its free abelian quotient, called the Betti number. We show that any combination of the group's rank, co-rank, and Betti number within obvious constraints is realized for some finitely presented group (for Betti number equal to rank, the group can be chosen torsion-free). In addition, we show that the Betti number is additive...
Cyclic subgroup separability of certain HNN extensions.
(Cyclic) subgroup separability of HNN and split extensions
Décomposition d'un groupe en produit libre ou somme amalgamée.
Decomposition Theorems for Group Pairs.
Deformation and rigidity of simplicial group actions on trees.
Descending Chains in Free Products.
Die Untergruppen der freien Produkte von beliebigen Gruppen
Direct products with isomorphic lattices
Eine Bemerkung zu den Nielsen-Transformationen.
Embeddings of graph braid and surface groups in right-angled Artin groups and braid groups.
Ends and Amalgamated Free Products of Groups.
Equalizers and coactions of groups
If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism . A right inverse (section) of is called a coaction on G. In this paper we study and the sections of . We consider the following topics: the structure of as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and the resulting...
Equivariant outer space and automorphisms of free-by-finite groups.
Existentially closed -groups
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
Free Products of Hopf Groups.
Free products of topological groups with equal uniformities, I