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.

In [Kim], Kimura introduced the notion of a “finite dimensional” motive (which we will refer to as “Kimura-finite” motive) and he conjectured that all Q-linear motives modulo rational equivalence are Kimura-finite. The same notion was introduced independently in a different context by O’Sullivan. Kimura-finiteness has been the subject of several articles recently ([GP02], [GP], [AK02]). In [GP]...