幂交换幂幂r幂群

Groups Complex. Cryptol. Pub Date : 1900-01-01 DOI:10.1515/GCC.2009.297

S. Majewicz, Marcos Zyman

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引用次数: 7

摘要

如果R是二项式环，则幂零R幂群G称为幂可交换群，如果对于任意α∈R， [G α， h] = 1，则当G α≠1时，[G, h] = 1。在本文中，我们进一步对幂零r幂群理论做出了贡献。特别地，我们证明了如果G是有限型的幂零R幂群，且对于任意素数π∈R不属于有限π型，则G是PC当且仅当它是一个阿贝尔R群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Power-Commutative Nilpotent R-Powered Groups

If R is a binomial ring, then a nilpotent R-powered group G is termed power-commutative if for any α ∈ R, [gα, h] = 1 implies [g, h] = 1 whenever gα ≠ 1. In this paper, we further contribute to the theory of nilpotent R-powered groups. In particular, we prove that if G is a nilpotent R-powered group of finite type which is not of finite π-type for any prime π ∈ R, then G is PC if and only if it is an abelian R-group.

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Groups Complex. Cryptol.

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