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Minimal and invariable generation of finite groups and a conjecture of Pyber

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  • UserGareth Tracey, University of Warwick
  • ClockFriday 09 October 2015, 15:00-16:00
  • HouseCMS, MR15.

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Suppose that G is a transitive permutation group, of degree n, but that G needs a large number of generators (in terms of n). If possible, we would like to “reduce” the number of generators, whilst keeping our group transitive. More precisely, we would like to take a subset X of G, minimal with the property that X is transitive. The question is: can we find a good upper bound for |X|, in terms of n? In this talk, we discuss the history of this question, including an old conjecture of Pyber, and some new results. We will also speak briefly about a generalisation of the minimal generation problem for finite groups, which has started to attract some recent work.

This talk is part of the Junior Algebra and Number Theory seminar series.

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