Abstract

We continue research into the cyclically presented groups with length three positive relators. We study small cancelation conditions, SQ-universality, and hyperbolicity, we obtain the Betti numbers of the groups’ abelianisations, we calculate the orders of the abelianisations of some groups, and we study isomorphism classes of the groups. Through computational experiments we assess how effective the abelianisation is as an invariant for distinguishing non-isomorphic groups.

中文翻译：

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长度为三个正相关的周期性呈现群的调查

摘要

我们继续研究长度为三个正相关的周期性呈现组。我们研究了小抵消条件、SQ 普遍性和双曲线，我们获得了群阿贝尔化的 Betti 数，我们计算了一些群的阿贝尔化的阶数，我们研究了群的同构类。通过计算实验，我们评估了阿贝尔化作为区分非同构群的不变量的有效性。