Geometric Group Theory - 2020

is a joint Düsseldorf - Gliwice seminar organized in October 2020

Questions and Comments

1. One comment on a role of Continuum Hypothesis in group theory.
2. A comment about elementarily equivalent groups.
3. A direct short proof of the fact that S_3 cannot be a subgroup of a quasi-finite group.
4. a) A short proof that the Thue-Morse sequence is cubefree is contained
   in the book of Lothaire "Algebraic combinatorics on words" (Proposition 3.1.1).
   b) A short proof that there exists a squarefree sequence in the alphabet a,a^{-1}, b, b^{-1}
   is contained in the paper of Adian:
   Адян С. И., Проблема Бернсайда и связанные с ней вопросы, УМН, том 65, выпуск 5(395) (2010), 5-60.
   It seems that this proof contains misprints (see formula (5) there).
5. A question about elementary equivalence and acylindricity.
6. A short survey on the elementary equivalence in the classes of finite-by-nilpotent and virtually free groups.
7. Pictures explaining distinguished systems of contiguity submaps and their graphs..