in this article, we consider some new classes of groups, namely, mp-groups, t0-groups,ø-groups,ø0-groups, groups with finitely embedded involution, which were appeared at the end of twenties century. these classes of infinite groups with finiteness conditions were introduced by v.p. shunkov. we give some review of new results on these classes of groups.

This paper studies several aspects of asymptotically hyperbolic Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed con...