Periodic subgroups of projective linear groups in positive characteristic

被引：0

作者：

Detinko, Alla S. ^{[1
]}

Flannery, Dane L. ^{[1
]}

机构：

[1] Natl Univ Ireland, Dept Math, Galway, Ireland

来源：

CENTRAL EUROPEAN JOURNAL OF MATHEMATICS | 2008年 / 6卷 / 03期

基金：

爱尔兰科学基金会;

关键词：

linear group; periodic group; projective general linear group; field; classification;

D O I：

10.2478/s11533-008-0033-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify the maximal irreducible periodic subgroups of PGL(q; F), where F is a field of positive characteristic p transcendental over its prime subfield, q not equal p is prime, and F-x has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q; F) containing the centre Fx1(q) of GL(q; F), such that G/Fx1(q) is a maximal periodic subgroup of PGL(q; F), and if H is another group of this kind then H is GL(q; F)-conjugate to a group in the list. We give criteria for determining when two listed groups are conjugate, and show that a maximal irreducible periodic subgroup of PGL(q; F) is self-normalising.

引用

页码：384 / 392

页数：9

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