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arXiv · 2610.17954

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

Omar Al-Raisi·Mohammad Shahryari
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Abstract

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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Omar Al-Raisi, Mohammad Shahryari. 2026-10-13. $\mathrm{CS}\mathfrak{X}$-groups and free constructions. https://arxiv.org/abs/2610.17954

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