Call a finitely generated group G to possess the property P with respect to a nonzero commutative ring R with unit element, if the cohomological dimension  of G is not greater than 1. In this paper, we show that if G is a group acting on a tree X without inversions such that for each vertex v of X, the vertex group  of v has the property P, the edge group  of each edge e of X is finite and the quotient graph  for the action of G on X is finite, then G has the property P. As an application, we show that if    is a tree product of the groups  with amalgamation subgroups  such that each  has the property P,  is finite,  and I is finite, then A has the property P. Furthermore, if  is the HNN group    of basis G and associated pairs  of isomorphic subgroups of G such that G has the property P,  is finite, and I is finite, then  has the property P.

groups acting on trees, cohomology of groups, tree product of groups, HNN groups.