Properties of groups with points

In this paper, we consider groups with points which were introduced by V.P. Shunkov in 1990. In Novikov-Adianʹs group, Adianʹs periodic products of finite groups without involutions and Olshanskyʹs periodic monsters every non-unit element is a point. There exist groups without points. In this article we shall prove some properties of the groups with points.