含五阶圈的特征标维数图  

The Character Degree Graph with Fifth-order Circles

作　　者：张先休[1] 张广祥[2] 

机构地区：[1]六盘水师范学院数学系,贵州六盘水553001 [2]西南大学数学与统计学院,重庆400715

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2013年第3期271-273,279,共4页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(61170120);六盘水师范学院科研基金项目(LPSSY201012);六盘水师范学院数学教育教学团队(LPSSYjxtd201102)

摘　　要：如果所有特征标维数图与Δ(G)同构的可解群的Fitting高存在共同的上界,则称Δ(G)为Fitting高有界的特征标维数图.由此可以猜想:设G是一个可解群,如果特征标维数图Δ(G)的Fitting高有界,那么G的Fitting高不大于4.已经有文献证明这个猜想在两种情形下是成立的.利用上述方法和结论,证明了一个含五阶圈的特征标维数图对应的有限可解群的Fitting高最多是4,并讨论了一类含五阶圈的特征标维数图的性质.By a definition of M. L. Lewis, a degree graph △ has bounded Fitting height if there is a bound on the Fitting height for the solvable group G with △（G）=△. And Lewis has a conjecture that if G be a solvable group where △（G） is a graph with hounded Fitting height,then Ghas Fitting height at most 4. Lewis has proved that the conjecture is right at least in the two situations. Methods and conclusions of Lewis are exploited in this paper,and the authors have done some work on the discussion of classification for the graphics. The authors prove that the Fitting height of a finite solvable group that has a character degree graph with fifth-order circles is at most 4,and they also discuss on the property of a kind of charac- ter degree graph with fifth-order circles.

关 键 词：Fitting高 特征标维数图 五阶圈 可解群 

分 类 号：O152.6[理学—数学]