Heiko Dietrich: Canonical presentations for finite solvable groups
Abstract: We define and describe how to compute canonical group presentations for finite solvable groups, such that two finite solvable groups are isomorphic if and only if they have the same canonical presentation. Our approach is motivated by O'Brien's (1993) canonical presentations for groups of prime power order and utilises ideas from group cohomology first described by Robinson (1982), Smith (1994), and Holt (2001). This is part of a larger project concerned with group identification and construction-by-ID.
Florian Lehner, TBA
Cheryl Praeger, TBA
Kamilla Rekvenyi: The orbital diameter of primitive permutation groups
Abstract: Let G be a group acting transitively on a finite set Ω. Then G acts on Ω ×Ω componentwise. Define the orbitals to be the orbits of G on Ω ×Ω. The diagonal orbital is the orbital of the form ∆= {(α, α)|α∈Ω}. The others are called non-diagonal orbitals. Let Γ be a non-diagonal orbital. Define an orbital graph to be the non-directed graph with vertex set Ω and edge set (α, β) ∈Γ with α, β∈Ω. If the action of G on Ω is primitive, then all non-diagonal orbital graphs are connected. The orbital diameter of a primitive permutation group is the supremum of the diameters of its non-diagonal orbital graphs. There has been a lot of interest in finding bounds on the orbital diameter of primitive permutation groups. In my talk I will outline some important background information and the progress made towards finding explicit bounds on the orbital diameter. In particular, I will discuss some results on the orbital diameter of the groups of simple diagonal type and their connection to the covering number of finite simple groups. I will also discuss some results for affine groups, which provides a nice connection to the representation theory of quasisimple groups. Finally, I will discuss some results for almost simple groups, which is joint work with Attila Maróti.
Anne Thomas, TBA
Stephan Tornier, TBA
George Willis, NTBA
TBA