论文标题
有限群体字符的平均零数
Average number of zeros of characters of finite groups
论文作者
论文摘要
人们对平均字符程度如何影响有限群的结构引起了人们的兴趣。我们定义，并用$ \ mathrm {anz}（g）$表示，有限组$ g $的字符的平均零数量为$ g $的字符表中的零数，除以$ g $的不可约性字符的数量。我们表明，如果$ \ mathrm {anz}（g）<1 $，则组$ g $是可解决的，并且如果$ \ mathrm {anz}（g）（g）（g）<\ frac {1} {2} {2} $，则$ g $是可取代的。我们通过证明$ \ mathrm {anz}（g）<\ frac {1} {3} $（如果$ g $是Abelian）来表征Abelian组。
There has been some interest on how the average character degree affects the structure of a finite group. We define, and denote by $ \mathrm{anz}(G) $, the average number of zeros of characters of a finite group $ G $ as the number of zeros in the character table of $ G $ divided by the number of irreducible characters of $ G $. We show that if $ \mathrm{anz}(G) < 1 $, then the group $ G $ is solvable and also that if $ \mathrm{anz}(G) < \frac{1}{2} $, then $ G $ is supersolvable. We characterise abelian groups by showing that $ \mathrm{anz}(G) < \frac{1}{3} $ if and only if $ G $ is abelian.
