Abstract
During the talk I will discuss a problem concerning extensions of
partial isomorphisms of finite tournaments and its equivalent form,
which is a problem about the pro-odd topology on the fee group. The
pro-odd topology is the refinement of the pro-finite topology where we
take only the normal subgroups of odd index as the neighborhood basis
of 1. The problem concerns a characterization of those finitely
generated subgroups of the free group which are closed in the pro-odd
topology. I will discuss a positive answer for cyclic subgroups and a
negative answer for a generalized version of this question. Joint work
with J. Huang, M. Pawliuk and D. Wise.