Abstract The aim of this paper is to compute the commutativity degree in polygroup’s theory, more exactly for the polygroup PG and for extension of polygroups by polygroups, obtaining boundaries for them. Also, we have analyzed the nilpotencitiy of 𝒜[𝒝], meaning the extension of polygroups 𝒜 and 𝒝.

中文翻译：

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多元群理论的新方面

摘要 本文的目的是计算polygroup 理论中的交换度，更准确地计算polygroup PG 和polygroups 通过polygroups 的扩展，获得它们的边界。此外，我们还分析了𝒜[𝒝] 的幂零性，即多群𝒜 和𝒝 的扩展。