Groups with few class sizes and the centraliser equality subgroup

Mann A

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Groups with few class sizes and the centraliser equality subgroup

机译：班级人数少的组和扶正器平等子组

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Let G be a p-group whose conjugacy classes have at most k sizes. We prove that G is abelian-by- (exponent p(k-1)) (if p = 2, exponent 2(k-2)). It follows that a 2-group with three class sizes is metabelian. Various other results on class sizes are proved, and some conjectures are formulated.

机译：令G为其共轭类别最多为k个大小的p-群。我们证明G是abelianby-by-（指数p（k-1））（如果p = 2，指数2（k-2））。因此，具有三个班级大小的2组是metabelian。证明了关于班级人数的其他各种结果，并提出了一些猜想。

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来源
《Israel Journal of Mathematics》 |2004年第0期|共14页
作者
Mann A;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
FINITE P-GROUPS; PRIME POWER ORDER; CONJUGACY CLASSES; BREADTH;

机译：有限P组;基本幂阶;共轭类;宽度;

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1. Groups with few class sizes and the centraliser equality subgroup [J] . Avinoam Mann Israel Journal of Mathematics . 2004,第1期

机译：班级人数少的组和扶正器平等子组
2. Equalities on the number of conjugacy classes of the Sylow p-subgroups of GL(n, q) [J] . Vera-Lopez A., Arregi J. M., Ormaetxea Leyre, Israel Journal of Mathematics . 2016,第Pta2期

机译：GL（n，q）的Sylow p-子群的共轭类数的等式
3. Character Degrees, Class Sizes, and Normal Subgroups of a Certain Class of p-Groups [J] . Jeffrey M. Riedl Journal of Algebra . 1999,第1期

机译：一类p-组的字符度，类大小和普通子组
4. A GENERALISATION ON THE SOLVABILITY OF FINITE GROUPS WITH THREE CLASS SIZES FOR NORMAL SUBGROUPS [C] . ANTONIO BELTRáN, MARíA JOSé FELIPE Groups St Andrews Theory Conference . 2015

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5. Small sample tests for the equality of intraclass correlation coefficients under unequal family sizes. [D] . Fujiwara, Koji. 2009

机译：在不平等的家庭规模下，对类内相关系数的相等性进行小样本测试。
6. Effect sizes of the differences between means without assuming variance equality and between a mean and a constant [O] . Satoshi Aoki 2020

机译：在不假设方差相等的情况下均值之间的差异以及均值和常数之间的差异的影响大小
7. Character Degrees, Class Sizes, and Normal Subgroups of a Certain Class of p-Groups [O] . Riedl Jeffrey M. 1999

机译：一类p-组的字符度，类大小和普通子组

Groups with few class sizes and the centraliser equality subgroup

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