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arXiv · 2506.12146

Structural Results On The Weak Commutativity Construction

Guilherme Ortega·Raimundo Bastos·Ricardo de Oliveira
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Abstract

The weak commutativity group $\chi(G)$ is generated by two isomorphic groups $G$ and $G^{\varphi }$ subject to the relations $[g,g^{\varphi}]=1$ for all $g \in G$. We obtain new expressions for the terms of the derived series and the lower central series of $\chi(G)$. We also present new bounds for the exponent of some sections of $\chi(G)$.

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Guilherme Ortega, Raimundo Bastos, Ricardo de Oliveira. 2025-06-13. Structural Results On The Weak Commutativity Construction. https://arxiv.org/abs/2506.12146

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