Leonov Y. The problem of conjugrtion and period's growth in Grigorchuk's groups

In the dissertation work we investigate Grigorchuk's 2-groups and some other finite generated residually finite groups of same construction. We suggest certain procedure for obtaining information about structure of elements in Grigorchuk's groups. In particular, we completely solve conjugace problem of elements in Grigorchuk's groups; we establish lower and upper estimation for period's growth in 2-groupsof Grigorchuk. Common approach during investigation of all Grigorchuk's groups allows expanding the class of groups that are investigated: we obtain necessary coditions for existing of identities in finite generated residually finite groups from which follows that there is no identities in Grigorchuk's groups.