Variations on the Baer-Suzuki theorem

被引：10

作者：

Guralnick, Robert ^{[1
]}

Malle, Gunter ^{[2
]}

机构：

[1] Univ So Calif, Dept Math, Los Angeles, CA 90089 USA

[2] TU Kaiserslautern, FB Math, D-67653 Kaiserslautern, Germany

来源：

MATHEMATISCHE ZEITSCHRIFT | 2015年 / 279卷 / 3-4期

基金：

美国国家科学基金会;

关键词：

Baer-Suzuki theorem; Conjugacy classes; Commutators; CONJUGACY CLASSES; CHARACTER TABLES; FINITE-GROUPS; SUBGROUPS;

D O I：

10.1007/s00209-014-1399-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The Baer-Suzuki theorem says that if is a prime, is a -element in a finite group and is a -group for all , then the normal closure of in is a -group. We consider the case where is replaced by for some other -element . While the analog of Baer-Suzuki is not true, we show that some variation is. We also answer a closely related question of Pavel Shumyatsky on commutators of conjugacy classes of -elements.

引用

页码：981 / 1006

页数：26

共 16 条

[1] Weakly subnormal subgroups and variations of the Baer-Suzuki theorem
Guralnick, Robert M.
Tong-Viet, Hung P.
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JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2025, 111 (01):
[2] Baer-Suzuki theorem for the π-radical
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ISRAEL JOURNAL OF MATHEMATICS, 2021, 245 (01) : 173 - 207
[3] Variations on the Baer–Suzuki theorem
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[4] A SOLVABLE VERSION OF THE BAER-SUZUKI THEOREM
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[5] Baer-Suzuki theorem for the solvable radical of a finite group
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[6] The Baer-Suzuki Theorem for Groups of 3-Exponent 1
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[7] On the sharp Baer-Suzuki theorem for the π-radical of a finite group
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[8] An analog of the Baer-Suzuki theorem for infinite groups
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[9] ON BAER-SUZUKI π-THEOREMS
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SIBERIAN MATHEMATICAL JOURNAL, 2011, 52 (02) : 340 - 347
[10] On Baer-Suzuki π-theorems
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Siberian Mathematical Journal, 2011, 52 (2) : 340 - 347

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