Closedness of a class of groups under free product.
Cohomology with free coefficients of the fundamental group of a graph of groups.
Combination of convergence groups.
Commensurability of graph products.
Complete growth series and products of groups.
Conjugacy pinched and cyclically pinched one-relator groups.
Here we consider two classes of torsion-free one-relator groups which have proved quite amenable to study-the cyclically pinched one-relator groups and the conjugacy pinched one-relator groups. The former is the class of groups which are free products of free groups with cyclic amalgamations while the latter is the class of HNN extensions of free groups with cyclic associated subgroups. Both are generalizations of surface groups. We compare and contrast results in these classes relative to n-freeness,...
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.