Projects per year
Abstract
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.
Original language  English 

Pages (fromto)  371392 
Number of pages  22 
Journal  Israel Journal of Mathematics 
Volume  198 
Issue number  1 
Early online date  1 Jul 2013 
DOIs  
Publication status  Published  Nov 2013 
Keywords
 Probability
 Finite simple group
 Direct products
 Profinite groups
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Dive into the research topics of 'The probability of generating a finite simple group'. Together they form a unique fingerprint.Projects
 2 Finished

Solving word problems: Solving word problems via generalisations of small cancellation
RoneyDougal, C. & Neunhoeffer, M.
1/10/11 → 30/09/14
Project: Standard

Automata Languages Decidability: Automata, Languages, Decidability in Algebra
1/03/10 → 31/05/14
Project: Standard