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SUMMARY:Discrete and free two-generated subgroups of SL2 - Matthew Conder\
 , University of Cambridge
DTSTART:20190125T150000Z
DTEND:20190125T160000Z
UID:TALK118705@talks.cam.ac.uk
CONTACT:Stacey Law
DESCRIPTION:Two-generated subgroups of SL(2\,R) have been widely studied i
 n the literature\, using the action of SL(2\,R) on the hyperbolic plane vi
 a Möbius transformations. In particular\, there exists a practical algori
 thm which\, given any two elements of SL(2\,R)\, determines after finitely
  many steps whether or not the subgroup they generate is discrete and free
  of rank two. Does such an algorithm exist for SL2 defined over other loca
 lly compact fields? In this talk we answer this question for the case of a
  non-archimedean local field K. Using the action of the group SL(2\,K) on 
 the Bruhat-Tits tree\, we construct an original and practical algorithm wh
 ich determines after finitely many steps whether or not any given two-gene
 rated subgroup of SL(2\,K) is discrete and free of rank two.
LOCATION:CMS\, MR14
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