naa a22 4500 510782256 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0034-7 doi (NATIONALLICENCE)springer-10.1007/s11856-013-0034-7 The probability of generating a finite simple group [Elektronische Daten] [Nina Menezes, Martyn Quick, Colva Roney-Dougal] We study the probability of generating a finite simple group, together with its generalisation P G,socG (d), the conditional probability of generating an almost simple finite group G by d elements, given that these elements generate G/socG. We prove that P G,socG (2) ⩽ 53/90, with equality if and only if G is A6 or S6, and establish a similar result for P G,socG (3). Positive answers to longstanding questions of Wiegold on direct products, and of Mel'nikov on profinite groups, follow easily from our results. Hebrew University Magnes Press, 2013 Menezes Nina School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, UK aut Quick Martyn School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, UK aut Roney-Dougal Colva School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, UK aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 371-392 0021-2172 198:1<371 2013 198 11856 https://doi.org/10.1007/s11856-013-0034-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0034-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Menezes Nina School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, UK aut NATIONALLICENCE 700 1- Quick Martyn School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, UK aut NATIONALLICENCE 700 1- Roney-Dougal Colva School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, Scotland, UK aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 371-392 0021-2172 198:1<371 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer