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This is a Quantitative Study study.

October 9, 2025Open Access

Beyond graph products and cactus groups: quandle products of groups

Key Points

Quandle products of groups showcase unique geometric properties through quasi-median Cayley graphs, enhancing group theory.
The introduction of quandle products expands the family of groups, including familiar types like cactus groups and wreath products.
Employing geometric methods allows for the deduction of significant information about the algebraic structure of quandle products.
These findings suggest potential applications and further exploration within the broader context of group theory and geometry.

Abstract

In this paper, we introduce and initiate the study of quandle products of groups, a family of groups that includes graph products of groups, cactus groups, wreath products, and the recently introduced trickle groups. Our approach is geometric: we show that quandle products admit quasi-median Cayley graphs; and, then, we exploit this geometry to deduce various valuable information about quandle products.

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Cite This Study

Anthony Genevois (Wed,) studied this question.

synapsesocial.com/papers/68e82b12e7fc21a30050041f https://doi.org/https://doi.org/10.48550/arxiv.2505.09194

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