SUMMARY OF THE RESEARCH PROPOSAL by Maxim Vsemirnov Research topic: Hurwitz and (2,3)-generated matrix groups and related problems. ... The reason to study these groups arises from the fact that the class of (2, 3)-generated groups together with three cyclic groups {1}, C2 and C3 is exactly the class of quotients of the classical modular group PSL2 (Z). ... The answer is known for sporadic groups, some exceptional groups of Lie type and for the most series of classical matrix groups of large rank. ...