Mini-Workshop: Amalgams for Graphs and Geometries
نویسنده
چکیده
On the classification of distance-transitive graphs
منابع مشابه
A CHARACTERISATION OF WEAKLY LOCALLY PROJECTIVE AMALGAMS RELATED TO A16 AND THE SPORADIC SIMPLE GROUPS M24 AND He
A simple undirected graph is weakly G-locally projective, for a group of automorphisms G, if for each vertex x, the stabiliser G(x) induces on the set of vertices adjacent to x a doubly transitive action with socle the projective group Lnx(qx) for an integer nx and a prime power qx. It is G-locally projective if in addition G is vertex transitive. A theorem of Trofimov reduces the classificatio...
متن کاملSymmetric Graphs of Valency
In this thesis we classify primitive amalgams of degree (5,2) and thereby obtain a description of symmetric graphs of valency 5. There are 22 such amalgams, and together with this list, we find the presentations for the universal completions of such amalgams and an example of a faithful finite completion in each case. Our methods include group theory, the amalgam method and some modular represe...
متن کاملGroup amalgams of index (4, 2) and 4-valent 2-arc-transitive graphs
A finite group amalgam of index (k,m) is a 5-tuple (L,φ,B, ψ,R) where L, B, and R are finite groups, φ : B → L and ψ : B → R are monomorphisms, and the indices of B and B in L and R are k and m, respectively. The amalgam is faithful if N ≤ B, N C L, and N C R implies N = 1. It is well known that the finite faithful amalgams of index (k, 2) are in a bijective correspondence with (the conjugacy c...
متن کاملAlgorithmic Problems in Amalgams of Finite Groups
Geometric methods proposed by Stallings [53] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [4, 25, 37, 38, 43, 48, 56]. It turns out that Stallings’ methods can be effectively generalized for the class of amalgams of finite groups [39]. In the present paper we employ subgroup gr...
متن کاملOn the Phan system of the Schur cover of SU(4, 32)
This article is part of the program described in [3]. We study the Phan amalgams and their universal completions that occur for q = 3 in rank n = 3 for the diagram A3 = D3, corresponding to SU(4, 3) ∼= Spin−(6, 3). We show that the associated geometries admit universal 9-fold coverings, by showing that the universal completion of the Phan amalgam is the central extension of SU(4, 3) by its Schu...
متن کامل