• Mathematics
  • Published 2004

Bonds for the Derived Length of Solvable Groups

  title={Bonds for the Derived Length of Solvable Groups},
  author={Zhang Guang-xiang},
A theorem about bounds for the derived length of soluble group G is improved. And the following result is getten: Let G be solvable. (a) If GGL(2, 3)ㄧ (Z_3×Z_3), then dl(G)=5. (b) If G is a subgroups of the symmetric group S_n, and G be not (a). Then dl(G)≤(7/3)log_3 n. (c) Let V≠0 be a faithful and completely reducibleF[G]-module over an arbitrary field F. Set n=dim_F(V). Then dl(G)≤8+(7/3)log_3(n/8).