Characterizability of the group 2 D p(3) by its order components, where p . 5 is a prime number not of the form 2m + 1

The author will prove that the group 2 D p (3) can be uniquely determined by its order components, where p . 2m + 1 is a prime number, p . 5. More precisely, if OC(G) denotes the set of order components of G, we will prove OC(G) = OC(2 D p (3)) if and only if G is isomorphic to 2 D p (3). A main consequence of our result is the validity of Thompson.s conjecture for the groups under consideration.