Some examples of Tychonoff groups

In this paper we survey the Tychono. property for discrete groups. General results and relations with amenability, with discrete potential theory (random walks), and with the theory of weights and of characters are discussed. We then present a characterization of Tychonoff property for virtually abelian groups, for polycyclic groups, and for linear groups. We also consider the case of metabelian groups, and several examples are given.