Factor groups of G6,6,6 through coset diagrams for an action on PL (Fq)

Factor groups of G6, 6, 6 through coset diagrams for an action on PL (Fq)

On Generating Coset Representatives of PGL2(Fq) in PGL2(Fq2)

There are q+q right PGL2(Fq)−cosets in the group PGL2(Fq2). In this paper, we present a method of generating all the coset representatives, which runs in time Õ(q), thus achieves the optimal time complexity up to a constant factor. Our algorithm has applications in solving discrete logarithms and finding primitive elements in finite fields of small characteristic.

Partial proof of Graham Higman's conjecture related to coset diagrams

Graham Higman has defined coset diagrams for PSL(2,ℤ). These diagrams are composed of fragments, and the fragments are further composed of two or more circuits. Q. Mushtaq has proved in 1983 that existence of a certain fragment γ of a coset diagram in a coset diagram is a polynomial f in ℤ[z]. Higman has conjectured that, the polynomials related to the fragments are monic and for a fixed degree...

Cayley graphs and coset diagrams

Let G be a finite group, and X a subset of G. The Cayley graph of G with respect to X , written Cay(G,X) has two different definitions in the literature. The vertex set of this graph is the group G. In one definition, there is an arc from g to xg for all g ∈ G and x ∈ X ; in the other definition, for the same pairs (g,x), there is an arc from g to gx. Cayley graphs are generalised by coset grap...

Coset Intersection Graphs for Groups

Let H,K be subgroups of G. We investigate the intersection properties of left and right cosets of these subgroups. If H and K are subgroups of G, then G can be partitioned as the disjoint union of all left cosets of H, as well as the disjoint union of all right cosets of K. But how do these two partitions of G intersect each other? Definition 1. Let G be a group, and H a subgroup of G. A left t...