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This bound is best possible and we present more detailed results for each family of exceptional groups, which allows us to determine the groups with [Formula: see text]. This extends recent work of Liebeck and Shalev, who established the bound [Formula: see text] for every almost simple primitive group of degree [Formula: see text] with socle [Formula: see text] (with a prescribed list of exceptions). Finally, by combining our results with the Lang\u2013Weil estimates from algebraic geometry, we determine bounds on a natural analogue of involution fixity for primitive actions of exceptional algebraic groups over algebraically closed fields.<\/jats:p>","DOI":"10.1142\/s0218196718500200","type":"journal-article","created":{"date-parts":[[2018,3,19]],"date-time":"2018-03-19T08:18:03Z","timestamp":1521447483000},"page":"411-466","source":"Crossref","is-referenced-by-count":10,"title":["On the involution fixity of exceptional groups of Lie type"],"prefix":"10.1142","volume":"28","author":[{"given":"Timothy C.","family":"Burness","sequence":"first","affiliation":[{"name":"School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK"}]},{"given":"Adam R.","family":"Thomas","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK"},{"name":"The Heilbronn Institute for Mathematical Research, Bristol, UK"}]}],"member":"219","published-online":{"date-parts":[[2018,6,28]]},"reference":[{"key":"S0218196718500200BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388470"},{"key":"S0218196718500200BIB002","doi-asserted-by":"publisher","DOI":"10.1017\/S0027763000017438"},{"key":"S0218196718500200BIB003","doi-asserted-by":"publisher","DOI":"10.2307\/2006997"},{"key":"S0218196718500200BIB004","doi-asserted-by":"publisher","DOI":"10.1112\/S1461157015000030"},{"key":"S0218196718500200BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(71)90008-1"},{"key":"S0218196718500200BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF01444035"},{"key":"S0218196718500200BIB009","doi-asserted-by":"publisher","DOI":"10.1006\/jsco.1996.0125"},{"key":"S0218196718500200BIB010","volume-title":"Groupes et algebr\u00e8s de Lie, Chaps. et","author":"Bourbaki N.","year":"1968"},{"key":"S0218196718500200BIB011","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00270-9"},{"key":"S0218196718500200BIB012","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.05.025"},{"key":"S0218196718500200BIB013","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139059060"},{"key":"S0218196718500200BIB014","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/718"},{"key":"S0218196718500200BIB015","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/pdn024"},{"key":"S0218196718500200BIB016","series-title":"Pure and Applied Mathematics","volume-title":"Simple Groups of Lie Type","volume":"28","author":"Carter R. 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