Given a finite connected graph ${\Gamma} $ and a group $ G $ acting transitively on the
vertices of ${\Gamma} $, we prove that the number of vertices of ${\Gamma} $ and the …

A walk of length n in a graph is consistent if there exists an automorphism of the graph that
maps the initial n vertices to the final n vertices of the walk, preserving their order. In this …

Let be a connected-vertex-transitive graph, let be a vertex of and let be the permutation
group induced by the action of the vertex-stabilizer on the neighbourhood. The graph is said …

A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or
semiregular. Interest in this class of groups is motivated by two sources: problems arising in …

arxiv:2410.17828v1 [math.GR] 23 Oct 2024 Page 1 arxiv:2410.17828v1 [math.GR] 23 Oct
2024 DENSITY OF QUOTIENT ORDERS IN GROUPS AND APPLICATIONS TO LOCALLY-TRANSITIVE …

In this paper we study G-arc-transitive graphs Δ where the permutation group induced by the
stabiliser Gx of the vertex x on the neighbourhood Δ (x) satisfies the two conditions given in …

In this paper we are interested in lifting a prescribed group of automorphisms of a finite
graph via regular covering projections. Let $\Gamma $ be a finite graph and let $\mathrm …

We extend the Burger–Mozes theory of closed, nondiscrete, locally quasiprimitive
automorphism groups of locally finite, connected graphs to the semiprimitive case, and …

The distinguishing number of G\leqslant Sym (Ω) G⩽ Sym (Ω) is the smallest size of a
partition of Ω Ω such that only the identity of G fixes all the parts of the partition. Extending …

Bounding the covolume of lattices in products Page 1 Bounding the covolume of lattices in
products Pierre-Emmanuel Caprace and Adrien Le Boudec Compositio Math. 155 (2019) …