具有特殊特征标维数的有限p-群

Finite p-Groups with Special Degrees of Character

主要研究了特征标维数集合是{1,p^m}的有限p-群G,证明了若这类有限p-群G的幂零类大于或者等于3,则|G|≥p^3m+1.特别地,如果G的特征标维数集合与共轭类长度集合都是{1,p^m},那么G的幂零类是2且|G|≥p^3m.

In this paper,we study a finite p -groups with cd (G)={1,p^m}.We prove that |G|≥p^3m+1 if the nilpotent class of G is greater than 2.Especially,if cd (G)={1,p^m}=cs( G ),then the nilpotent class of G is 2 and |G|≥p^3m.