This problem was reported by Lei Chen.<\/p>\n
Lemma 2.37(ii) is not true if $\\mathfrak G$ is a digraph. Using the notation of the book, a $G$-vertex-transitive digraph $\\mathfrak G$ is $(G,2)$-arc-transitive if and only if $G_\\alpha$ factorises as $G_\\alpha=G_{\\alpha, \\alpha_1} G_{\\alpha,\\alpha_2}$ for a 2-arc $(\\alpha_1, \\alpha, \\alpha_2)$ (see for instance Lemma 2.1 in [GX]).<\/p>\n
This part of the lemma is only used for undirected graphs in the rest of the book and so this causes no problem in subsequent arguments.<\/p>\n
[GX] Michael Giudici and Binzhou Xia.\u00a0Vertex-quasiprimitive 2-arc-transitive digraphs.\u00a0Ars Mathematica Contemporanea, 14 (2018), 67\u201382.<\/p>\n","protected":false},"excerpt":{"rendered":"
This problem was reported by Lei Chen. Lemma 2.37(ii) is not true if $\\mathfrak G$ is a digraph. Using the notation of the book, a $G$-vertex-transitive digraph $\\mathfrak G$ is $(G,2)$-arc-transitive if and only if $G_\\alpha$ factorises as $G_\\alpha=G_{\\alpha, \\alpha_1} G_{\\alpha,\\alpha_2}$ for a 2-arc $(\\alpha_1, \\alpha, \\alpha_2)$ (see for instance Lemma 2.1 in [GX]). This … Continue reading Lemma 2.37<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":71,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages\/1156"}],"collection":[{"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/comments?post=1156"}],"version-history":[{"count":6,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages\/1156\/revisions"}],"predecessor-version":[{"id":1170,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages\/1156\/revisions\/1170"}],"up":[{"embeddable":true,"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/pages\/71"}],"wp:attachment":[{"href":"http:\/\/localhost\/index.php\/wp-json\/wp\/v2\/media?parent=1156"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}