Nilpotency of the derived subgroup of a finite tangled group

A. L. Myl’nikov

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Nilpotency of the derived subgroup of a finite tangled group

机译：有限缠结群的导出子群的幂等性

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摘要

We study finite groups whose every subset containing the identity and closed with respect to the operation x ○ y = xy~-1 x is a subgroup. We prove that the derived subgroup of such a group is nilpotent, which implies that the derived length of such a group is at most three.

机译：我们研究有限组，其每个子集均包含标识并且相对于操作x○y = xy〜-1 x闭合是一个子组。我们证明了该组的派生子群是幂零的，这意味着该组的派生长度至多为三个。

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来源
《Siberian Mathematical Journal》 |2006年第5期|共9页
作者
A. L. Myl’nikov;
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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
twisted subset; twisted subgroup; tangled subgroup;

机译：扭曲子集;扭曲子群;纠结子群;

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专利

1. Nilpotency of the derived subgroup of a finite tangled group [J] . A. L. Myl’nikov Siberian Mathematical Journal . 2006,第5期

机译：有限缠结群的导出子群的幂等性
2. Maximal subgroups of a sylow p-subgroup and p-nilpotency of finite groups [J] . Xu Y., Li X., Passman D. Journal of algebra and its applications . 2010,第3期

机译：sylow p-subgroup的最大子组和有限组的p-幂零
3. THE p-NILPOTENCY OF FINITE GROUPS WITH SOME WEAKLY PRONORMAL SUBGROUPS [J] . Liu Jianjun, Chang Jian, Chen Guiyun Czechoslovak Mathematical Journal . 2020,第3期

机译：具有一些弱电话子组的有限组的p-nilpotency
4. On the Nilpotency of Subgroups of Self-Homotopy Equivalences [C] . Martin Arkowitz, Gregory Lupton Barcelona Conference on Algebraic Topology . 1995

机译：关于自同型等效性亚组的尼利率
5. Derived lengths of solvable groups with abelian Sylow subgroups [D] . Marshall, Mary Kathleen. 1993

机译：带有Abelian Sylow子群的可解群的导出长度
6. Some subgroup embeddings in finite groups: A mini review [O] . A. Ballester-Bolinches, J.C. Beidleman, R. Esteban-Romero, 2015

机译：有限群中的一些子群嵌入：迷你评论
7. On nilpotency of higher commutator subgroups of a finite soluble group [O] . Josean da Silva Alves, Pavel Shumyatsky 2020

机译：关于有限度可溶性群体较高换向器亚组的尼序
8. Tangle-Free Finite Element Mesh Motion for Ablation Problems. [R] . Droba, J. 2016

机译：消融问题的无缠结有限元网格运动。

Nilpotency of the derived subgroup of a finite tangled group

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