On weak commutativity in groups

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• 作者：Dessislava Kochloukova^a ; ^b ; ^{desi@ime.unicamp.br" class="auth_mail" title="E-mail the corresponding author} ; Said Sidki^a ; ^b ; ^{s.n.sidki@mat.unb.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 20J05 ; secondary ; 20F05
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：471
• 期：Complete
• 页码：319-347
• 全文大小：511 K

文摘

For a group G   we study homological and homotopical properties of the group χ(G)=〈G,G^ψ|[g,g^ψ]=1 for g∈G〉$\chi (G)=〈G,G^{\psi }|[g,g^{\psi }]=1\text{for}g\in G〉$. In particular, we show that the operator χ   preserves the soluble of type FP_∞$F{P}_{\infty }$ property.