66 research outputs found
Alternating Quotients of Fuchsian Groups
It is shown that any finitely generated non-elementary Fuchsian group has
among its homomorphic images all but finitely many of the alternating groups.
This settles in the affirmative a conjecture of Graham Higman.Comment: 20 pages, 7 figure
Graphs, free groups and the Hanna Neumann conjecture
A new bound for the rank of the intersection of finitely generated subgroups
of a free group is given, formulated in topological terms, and very much in the
spirit of Stallings. The bound is a contribution to (although unfortunately not
a solution of) the strengthened Hanna Neumann conjecture.Comment: J. Group Theory (to appear
Partial mirror symmetry, lattice presentations and algebraic monoids
This is the second in a series of papers that develops the theory of
reflection monoids, motivated by the theory of reflection groups. Reflection
monoids were first introduced in arXiv:0812.2789. In this paper we study their
presentations as abstract monoids. Along the way we also find general
presentations for certain join-semilattices (as monoids under join) which we
interpret for two special classes of examples: the face lattices of convex
polytopes and the geometric lattices, particularly the intersection lattices of
hyperplane arrangements. Another spin-off is a general presentation for the
Renner monoid of an algebraic monoid, which we illustrate in the special case
of the "classical" algebraic monoids.Comment: 41 page
- …