Notes on Non-Vanishing Elements of Finite Solvable Groups

作者：He Liguo^*

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2012, 35(1): 163-169.

• Solvable group
• character
• Fitting subgroup
• non-vanishing element

Let G be a finite solvable group. The element p E C is said to be a non-vanishing element of G if chi(g) not equal 0 for all chi is an element of Irr (G). It is conjectured that all of non-vanishing elements of G lie in its Fitting subgroup F(G). In this note, we prove that this conjecture is true for nilpotent-by-supersolvable groups. Write V(G) to denote the subgroup generated by all non-vanishing elements of G, and F(n)(G) the nth term of the ascending Fitting series. It is proved that v(F(n)(G)) <= F(n-1) (G) whenever G is solvable. If this conjecture were not true, then it is proved that the minimal counterexample is a solvable primitive permutation group and the more detailed information is presented. Some other related results are proved.

• 出版日期2012
• 单位沈阳工业大学