A 1 1/2-dimensional version of Hopf's Theorem on the number of ends of a group.
A Bers-like proof of the existence of train tracks for free group automorphisms
Using Lipschitz distance on Outer space we give another proof of the train track theorem.
A certain property of abelian groups
A Characteristic 2-Subgroups of a Finite Special Group.
A Characterization of the Simple Group M24.
A class of generalized supersoluble groups.
A combinatorial problem in infinite groups.
A computer algebra solution to a problem in finite groups.
We report on a partial solution of the conjecture that the class of finite solvable groups can be characterised by 2-variable identities. The proof requires pieces from number theory, algebraic geometry, singularity theory and computer algebra. The computations were carried out using the computer algebra system SINGULAR.
A condition for the solvability of finite groups.
A condition on a certain variety of groups
A conjugacy theorem for subgroups of containing the group of diagonal matrices
A cyclically pinched product of free groups which is not residually free.
A Finitely Presented Solvable Group that is not Residually Finite.
A finiteness condition on automorphism groups
A free group acting without fixed points on the rational unit sphere
A free group of piecewise linear transformations
We prove the following conjecture of J. Mycielski: There exists a free nonabelian group of piecewise linear, orientation and area preserving transformations which acts on the punctured disk {(x,y) ∈ ℝ²: 0 < x² + y² < 1} without fixed points.
A Free Product with a Non-Power Amalgamated which is not Residually Free.
A generalized Frattini subgroup of a finite group.
A generalized Hopf formula for higher homology groups.
A geometric approach to on-diagonal heat kernel lower bounds on groups
We introduce a new method for obtaining heat kernel on-diagonal lower bounds on non- compact Lie groups and on infinite discrete groups. By using this method, we are able to recover the previously known results for unimodular amenable Lie groups as well as for certain classes of discrete groups including the polycyclic groups, and to give them a geometric interpretation. We also obtain new results for some discrete groups which admit the structure of a semi-direct product or of a wreath product....