{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,1,4]],"date-time":"2024-01-04T09:41:24Z","timestamp":1704361284295},"reference-count":17,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:p>Let [Formula: see text] be a permutation group on a set [Formula: see text]. A base for [Formula: see text] is a subset of [Formula: see text] whose pointwise stabilizer is trivial, and the base size of [Formula: see text] is the minimal cardinality of a base for [Formula: see text]. If [Formula: see text] has base size [Formula: see text], then the corresponding Saxl graph [Formula: see text] has vertex set [Formula: see text] and two vertices are adjacent if and only if they form a base for [Formula: see text]. A recent conjecture of Burness and Giudici states that if [Formula: see text] is a finite primitive permutation group with base size [Formula: see text], then [Formula: see text] has the property that every two vertices have a common neighbour. We investigate this conjecture in the case where [Formula: see text] is an affine group and a point stabilizer is an almost quasisimple group whose central quotient is either [Formula: see text] or [Formula: see text] for some sporadic simple group [Formula: see text]. We verify the conjecture for all but [Formula: see text] of the groups [Formula: see text].<\/jats:p>","DOI":"10.1142\/s0218196723500194","type":"journal-article","created":{"date-parts":[[2023,3,1]],"date-time":"2023-03-01T12:49:50Z","timestamp":1677674990000},"page":"369-389","source":"Crossref","is-referenced-by-count":1,"title":["Saxl graphs of primitive affine groups with sporadic point stabilizers"],"prefix":"10.1142","volume":"33","author":[{"given":"Melissa","family":"Lee","sequence":"first","affiliation":[{"name":"School of Mathematics, Monash University, Melbourne, Australia"}]},{"given":"Tomasz","family":"Popiel","sequence":"additional","affiliation":[{"name":"School of Mathematics, Monash University, Melbourne, Australia"}]}],"member":"219","published-online":{"date-parts":[[2023,4,11]]},"reference":[{"key":"S0218196723500194BIB001","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139175319","volume-title":"Finite Group Theory","author":"Aschbacher M.","year":"2000"},{"key":"S0218196723500194BIB002","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1112\/blms\/bdq096","volume":"43","author":"Bailey R. 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