Weakening incidence conditions for subgroups considered by algebraists from perm university

In the first part of this article incidence conditions, introduced and considered by algebraists from Perm University, and information about where and which class of groups are described by them, are given. In the second part, the results, received by algebraists from Perm University in considering of groups with several new generalizations of incidence conditions for noncyclic subgroups, are announced: the formulations of the 14 new theorems proved by them are given. The proofs of these theorems are supposed to be published in a series of separate articles.