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.