We present here some
theorems concerning the existence of one parameter subsemigroups in the
generalized differentiable semigroups introduced by Graham. These semigroups
are based on a type of generalized differentiable manifold and include as
examples many semigroups of matrices and subsemigroups of Lie groups which
are not ordinary manifolds. The multiplication function is required to be
strongly differentiable (a generalization of Frechet differentiability). We shed
some light on a question of Graham by showing that such locally complete
Ck monoids which contain C2 curves starting at 1 must contain Ck one
parameter subsemigroups. The argument shows that closed submonoids of Lie
groups which contain C2 curves with one end at 1 contain one parameter
subsemigroups.
