We relate the Mather invariant of diffeomorphisms (closed) interval to their asymptotic distortion. For maps with only parabolic fixed points, we show that former is trivial if and latter vanishes. As a consequence, obtain such diffeomorphism no point in interior contains identity closure its C1+bv conjugacy class it time-1 map C1 vector field. A corollary this do not arise from fields are undi...

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...