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SUMMARY:Conditional decision problems in group theory - Maurice Chiodo (Un
 iversity of Melbourne)
DTSTART:20090119T160000Z
DTEND:20090119T170000Z
UID:TALK16402@talks.cam.ac.uk
CONTACT:Anton Evseev
DESCRIPTION:Decision problems in group theory have been a topic of much in
 terest for some time. The standard formulation for such problems goes alon
 g the lines of “Given a finite group presentation P\, does there exist a
 n algorithm to determine some property of the group described by P?” For
  many such questions\, the answer is no. However\, in certain cases\, if t
 he collection of groups being considered is restricted to satisfying some 
 condition (say\, being abelian\, hyperbolic\, etc)\, then many of these de
 cision problems can be answered. In this talk I will give examples of such
  decision problems that are undecidable in general\, but can be decided wh
 en we impose further conditions. In addition to this\, I will outline othe
 r conditional decision problems whose decidability is (to the best of my k
 nowledge)\, still unknown. The most interesting such example is the follow
 ing (open) question: Given a finite presentation of a non-trivial group\, 
 can one algorithmically construct a non-trivial element?
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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