Series: Penn State Logic Seminar

Date: Tuesday, March 22, 2005

Time: 2:30 - 3:45 PM

Place: 103 Pond Laboratory

Speaker: Stephen G. Simpson, Penn State, Mathematics

Title: Residual Finiteness and the Word Problem for Groups


  Novikov 1955 and Boone 1959 have constructed finitely presented
  groups with unsolvable word problem.  Therefore, it is of interest
  to find sufficient conditions for a finitely presented group to have
  solvable word problem.  One such condition is residual finiteness:
  the intersection of all subgroups of finite index is trivial.  We
  prove that every finitely generated nilpotent group is finitely
  presented and residually finite (Hirsch 1946), hence has solvable
  word problem.  On the other hand, Kharlampovich 1981 has constructed
  a finitely presented solvable group with unsolvable word problem.
  We review some unpublished constructions of S. Aanderaa 1994 and
  H. Gravir 1995 which yield a Trakhtenbrot-style inseparability
  theorem for finitely presented groups.