Sylow 2-subgroups of rational solvable groups

被引：10

作者：

Isaacs, I. M. ^{[1
]}

Navarro, Gabriel ^{[2
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

[2] Univ Valencia, Dept Algebra, E-46100 Valencia, Spain

来源：

MATHEMATISCHE ZEITSCHRIFT | 2012年 / 272卷 / 3-4期

关键词：

Rational group; Sylow; 2-subgroup; 2-rational;

D O I：

10.1007/s00209-011-0965-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A long-standing conjecture proposes that a Sylow 2-subgroup S of a finite rational group must be rational. In this paper we provide a counterexample to this conjecture, but we show that if G is solvable and S has nilpotence class 2, then S actually is rational.

引用

页码：937 / 945

页数：9

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