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arXiv 2610.179542026-10-14math.GR

$\boldsymbol{\text{CS}\boldsymbol{\text{X}}}$群与自由构造

$\mathrm{CS}\mathfrak{X}$-groups and free constructions

Sultan Qaboos University（苏丹卡布斯大学）

Omar Al-Raisi, Mohammad Shahryari

备注：: 11 pages

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AI总结：

针对CSX群的极大X子群为malnormal的定义，证明无对合且具有malnormal融合的两个CSX群的融合自由积仍是CSX群，并据此给出CSX群的HNN扩张仍为CSX群的条件。

摘要：

设$\boldsymbol{\text{X}}$为群的一个簇，群$G$是$\boldsymbol{\text{CS}\boldsymbol{\text{X}}}$群，当且仅当它的极大$\boldsymbol{\text{X}}$-子群是 malnormal（正规子群）。我们证明：两个$\boldsymbol{\text{CS}\boldsymbol{\text{X}}}$群在具有 malnormal 融合且无对合的融合自由积仍是$\boldsymbol{\text{CS}\boldsymbol{\text{X}}}$群；利用该结论，我们描述了$\boldsymbol{\text{CS}\boldsymbol{\text{X}}}$群的 HNN 扩张仍为$\boldsymbol{\text{CS}\boldsymbol{\text{X}}}$群的条件。

英文摘要：

Let $\X$ be a variety of groups. A group $G$ is $\CSX$ if its maximal $\X$-subgroups are malnormal. We prove that the amalgamated free product of two $\CSX$-groups with a malnormal amalgam and without any involutions is again $\CSX$. Using this, we describe conditions under which the HNN-extension of a $\CSX$-group is $\CSX$.

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