ON THE MAXIMAL NUMBER OF COPRIME SUBDEGREES IN FINITE PRIMITIVE PERMUTATION GROUPS

被引：1

作者：

Dolfi, Silvio ^{[1
]}

Guralnick, Robert ^{[2
]}

Praeger, Cheryl E. ^{[3
]}

Spiga, Pablo ^{[4
]}

机构：

[1] Univ Florence, Dipartimento Matemat Ulisse Dini, Viale Morgagni 67-A, I-50134 Florence, Italy

[2] Univ Southern Calif, Dept Math, Los Angeles, CA 90089 USA

[3] Univ Western Australia, Sch Math & Stat, Ctr Math Symmetry & Computat, Crawley, WA 6009, Australia

[4] Univ Milano Bicocca, Dipartimento Matemat & Applicaz, Via Cozzi 55, I-20125 Milan, MI, Italy

来源：

ISRAEL JOURNAL OF MATHEMATICS | 2016年 / 216卷 / 01期

基金：

美国国家科学基金会;

关键词：

AUTOMORPHISM-GROUPS; LIE TYPE; EXCEPTIONAL GROUPS; SUBGROUPS;

D O I：

10.1007/s11856-016-1405-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The subdegrees of a transitive permutation group are the orbit lengths of a point stabilizer. For a finite primitive permutation group which is not cyclic of prime order, the largest subdegree shares a non-trivial common factor with each non-trivial subdegree. On the other hand, it is possible for non-trivial subdegrees of primitive groups to be coprime, a famous example being the rank 5 action of the small Janko group J (1) on 266 points which has subdegrees of lengths 11 and 12. We prove that, for every finite primitive group, the maximal size of a set of pairwise coprime non-trivial subdegrees is at most 2.

引用

页码：107 / 147

页数：41

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