关于𝑝-groups的弱交换性

Pub Date : 2023-06-15 DOI:10.1515/jgth-2022-0165

R. Bastos, E. de Melo, R. de Oliveira, C. Monetta

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引用次数: 0

摘要

摘要对所有G∈G G \in G，由两个同构群𝐺和G φ G^ {\varphi}根据关系[G, G φ]=1 [G, G^ {\varphi}]=1生成弱交换群χ≠(G) \chi (G)。当𝐺是有限的𝑝-group时，我们给出了χ¹(G) \chi (G)的指数及其截面的新边界。

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On weak commutativity in 𝑝-groups

Abstract The weak commutativity group χ ⁢ ( G ) \chi(G) is generated by two isomorphic groups 𝐺 and G φ G^{\varphi} subject to the relations [ g , g φ ] = 1 [g,g^{\varphi}]=1 for all g ∈ G g\in G . We present new bounds for the exponent of χ ⁢ ( G ) \chi(G) and its sections, when 𝐺 is a finite 𝑝-group.

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