On the isomorphism problem for 2-generator metabelian groups (Q795163)

Let p be an odd prime. Like in his earlier papers the author deals with the isomorphism problem for 2-generator metabelian p-groups. The general problem seems to be very difficult. In the present article the author defines a subclass of 2-generator groups which are 1-relator groups in the variety of metabelian groups of exponent p (the definition is rather technical). By the main theorem 1 each group from this subclass contains a pair of characteristic subgroups of index p. By theorem 2 this implies the solvability of the isomorphism problem for this subclass.