The probability of generating a finite simple group
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We study the probability of generating a finite simple group, together with its generalisation PG,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 PG,socG(2) ⩾ 53/90, with equality if and only if G is A6 or S6, and establish a similar result for PG,socG(3). Positive answers to longstanding questions of Wiegold on direct products, and of Mel’nikov on profinite groups, follow easily from our results.
Menezes , N E , Quick , M & Roney-Dougal , C M 2013 , ' The probability of generating a finite simple group ' Israel Journal of Mathematics , vol 198 , no. 1 , pp. 371-392 . DOI: 10.1007/s11856-013-0034-7
Israel Journal of Mathematics
© 2013 The Hebrew University Magnes Press, Jerusalem. Published by Springer. The final publication is available at Springer via http://dx.doi.org/10.1007/s11856-013-0034-7
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