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CATEGORIES:Junior Algebra/Logic/Number Theory seminar
SUMMARY:Conditional decision problems in group theory - Ma
urice Chiodo (University of Melbourne)
DTSTART;TZID=Europe/London:20090119T160000
DTEND;TZID=Europe/London:20090119T170000
UID:TALK16402AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/16402
DESCRIPTION:Decision problems in group theory have been a topi
c of much interest for some time. The standard for
mulation for such problems goes along the lines of
“Given a finite group presentation P\, does there
exist an algorithm to determine some property of
the group described by P?” For many such questions
\, the answer is no. However\, in certain cases\,
if the collection of groups being considered is re
stricted to satisfying some condition (say\, being
abelian\, hyperbolic\, etc)\, then many of these
decision 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 th
is\, I will outline other conditional decision pro
blems whose decidability is (to the best of my kno
wledge)\, still unknown. The most interesting such
example is the following (open) question: Given a
finite presentation of a non-trivial group\, can
one algorithmically construct a non-trivial elemen
t?
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0W
B
CONTACT:Anton Evseev
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