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University of Cambridge > Talks.cam > Junior Algebra/Logic/Number Theory seminar > Minimal and invariable generation of finite groups and a conjecture of Pyber

## Minimal and invariable generation of finite groups and a conjecture of PyberAdd to your list(s) Download to your calendar using vCal - Gareth Tracey, University of Warwick
- Friday 09 October 2015, 15:00-16:00
- CMS, MR15.
If you have a question about this talk, please contact nd332. 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/Logic/Number Theory seminar series. ## This talk is included in these lists:- All CMS events
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