A group of odd order G G with O p ( G ) = 1 {O_p}(G) = 1 has a block of defect less than [ n / 2 ] [n/2] , where p n = | G | p {p^n} = |G{|_p} . In addition, if G G is supersolvable by nilpotent, G G has a block of defect zero.

We recall the following definition (see [1]):A finite group G is said to be a Frobenius–Wielandt group provided that there exists a proper subgroup H of G and a proper normal subgroup N of H such that H∩Hg≦N if g∈G–H. Then H/N is said to be the complement of (G, H, N) (see [1] for more details and notation).