Hecke operators on the -analogue of group cohomology.
Let be a finite simple undirected graph with a subgroup of the full automorphism group . Then is said to be -transitive for a positive integer , if is transitive on -arcs but not on -arcs, and -transitive if it is -transitive. Let be a stabilizer of a vertex in . Up to now, the structures of vertex stabilizers of cubic, tetravalent or pentavalent -transitive graphs are known. Thus, in this paper, we give the structure of the vertex stabilizers of connected hexavalent -transitive...
We prove that the natural HNN-extensions of the fractional Fibonacci groups are the fundamental groups of high-dimensional knot complements. We also give some characterization and interpretation of these knots. In particular we show that some of them are 2-knots.
Highly transitive subgroups of the symmetric group on the natural numbers are studied using combinatorics and the Baire category method. In particular, elementary combinatorial arguments are used to prove that given any nonidentity permutation α on ℕ there is another permutation β on ℕ such that the subgroup generated by α and β is highly transitive. The Baire category method is used to prove that for certain types of permutation α there are many such possibilities for β. As a simple corollary,...