Let Γ be a connected G-vertex-transitive graph, let v be a vertex of Γ and let GvΓ(v) be the permutation group induced by the action of the vertex-stabilizer Gv on the neighbourhood Γ (v). The graph Γ is said to be G-locally primitive if GvΓ(v) is primitive. Weiss conjectured in 1978 that there exists a function f: N → N such that, if Γ is a connected G-vertex-transitive locally primitive graph of valency d and v is a vertex of Γ with /Gv/ finite, then /Gv/≤ f(d). As an application of the Local C(G,T) Theorem, we prove this conjecture when GvΓ(v) contains an abelian regular subgroup. In fact, we show that the point-wise stabilizer in G of a ball of Γ of radius 4 is the identity subgroup.
Spiga, P. (2015). An application of the Local C(G,T) Theorem to a conjecture of Weiss. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 48(1), 12-18 [10.1112/blms/bdv071].
Citazione: | Spiga, P. (2015). An application of the Local C(G,T) Theorem to a conjecture of Weiss. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 48(1), 12-18 [10.1112/blms/bdv071]. | |
Tipo: | Articolo in rivista - Articolo scientifico | |
Carattere della pubblicazione: | Scientifica | |
Presenza di un coautore afferente ad Istituzioni straniere: | No | |
Titolo: | An application of the Local C(G,T) Theorem to a conjecture of Weiss | |
Autori: | Spiga, P | |
Autori: | SPIGA, PABLO (Corresponding) | |
Data di pubblicazione: | 2015 | |
Lingua: | English | |
Rivista: | BULLETIN OF THE LONDON MATHEMATICAL SOCIETY | |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1112/blms/bdv071 | |
Appare nelle tipologie: | 01 - Articolo su rivista |
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