Class sizes of prime-power order p′-elements and normal subgroups

被引：0

作者：

Beltran, Antonio ^{[1
]}

Jose Felipe, Maria ^{[2
]}

Shao, Changguo ^{[3
]}

机构：

[1] Univ Jaume 1, Dept Matemat, Castellon de La Plana 12071, Spain

[2] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain

[3] Univ Jinan, Sch Math Sci, Jinan 250022, Shandong, Peoples R China

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2015年 / 194卷 / 05期

关键词：

Finite groups; Conjugacy class sizes; Normal subgroups; Prime-power order elements; p '-Elements; FINITE-GROUPS;

D O I：

10.1007/s10231-014-0432-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove an extension of the renowned Ito's theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p'-elements and prime-power order elements. Let N be a normal subgroup of a finite group G and let p be a fixed prime. Suppose that vertical bar x(G)vertical bar = 1 or m for every q-element of N and for every prime q not equal p. Then, N has nilpotent p-complements.

引用

页码：1527 / 1533

页数：7

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