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Abstract
A group L is primitive monolithic if L has a unique minimal normal subgroup, N , and trivial Frattini subgroup. By P_{L,N}(k) we denote the conditional probability that k randomly chosen elements of L generate L , given that they project onto generators for L/N. In this article we show that P_{L,N}(k) is controlled by P_{Y,S}(2), where N≅S^{r }and Y is a 2generated almost simple group with socle S that is contained in the normalizer in L of the first direct factor of N . Information about P_{L,N}(k) for L primitive monolithic yields various types of information about the generation of arbitrary finite and profinite groups.
Original language  English 

Pages (fromto)  413433 
Journal  Journal of Algebra 
Volume  407 
Early online date  18 Apr 2014 
DOIs  
Publication status  Published  1 Jun 2014 
Keywords
 Finite group theory
 Random generation of finite groups
 Finite simple groups
 Crownbased power
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Dive into the research topics of 'On the probability of generating a monolithic group'. Together they form a unique fingerprint.Projects
 1 Finished

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