可解群的导长的界

Bonds for the Derived Length of Solvable Groups

将关于可解群G的导长的界的定理改进为:G是可解群.(a)若G GL(2,3)晴 (Z3×Z3),则dl(G)=5.(b)若G≤Sn,且G不为情形(a),则dl(G)≤(7/3)log3n.(c)若V≠0是任意域F上的一忠实且完全可约F[G]模.令n=dimF(V),则dl(G)≤8+(7/3)log3(n/8).

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).