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SUMMARY:Minimal and invariable generation of finite groups and a conjectur
 e of Pyber - Gareth Tracey\, University of Warwick
DTSTART:20151009T140000Z
DTEND:20151009T150000Z
UID:TALK61535@talks.cam.ac.uk
CONTACT:43628
DESCRIPTION:Suppose that G is a transitive permutation group\, of degree n
 \, but that G needs a\nlarge number of generators (in terms of n). If poss
 ible\, we would like to “reduce” the number of\ngenerators\, whilst ke
 eping our group transitive. More precisely\, we would like to take a subse
 t\nX of G\, minimal with the property that X is transitive. The question i
 s: can we find a\ngood upper bound for |X|\, in terms of n? In this talk\,
  we discuss the history of this question\,\nincluding an old conjecture of
  Pyber\, and some new results.\nWe will also speak briefly about a general
 isation of the minimal generation problem for finite\ngroups\, which has s
 tarted to attract some recent work.
LOCATION:CMS\, MR15
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