A characterization of the group 2Dn(2), where n=2m+1≥5

In this paper it is proved that the group 2 D n (2), where n =2 m +1≥5, can be uniquely determined by its order components. More precisely we will prove that if G is a finite group and OC ( G ) denotes the set of order components of G , then OC ( G )= OC ( 2 D n (2)) if and only if G ≅ 2 D n (2). A main consequence of our result is the validity of Thompson’s conjecture for the group under consideration.