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Journals / International Electronic Journal of Algebra / 2026 / Volume: 37 Issue: 37

On the extension problem for gyrogroups

Teerapong Suksumran(Chiang Mai University)
Pages
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Publication Date
2025-01-14
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In particular, we refine the hierarchy of gyrogroup structure by showing that generic gyrogroups are extensions of contra-associative gyrogroups or g-extensive gyrogroups.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:A gyrogroup is an algebraic structure whose operation is in \mbox{general} non-associative and shares common properties with groups.
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Key Findings & Data:In this paper, we introduce two disjoint families of gyrogroups.
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Conclusion & Impact:In particular, we refine the hierarchy of gyrogroup structure by showing that generic gyrogroups are extensions of contra-associative gyrogroups or g-extensive gyrogroups.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Contra-associative gyrogroup · g-extensive gyrogroup · associator

Abstract

A gyrogroup is an algebraic structure whose operation is in \mbox{general} non-associative and shares common properties with groups. In this paper, we introduce two disjoint families of gyrogroups. One family consists of \mbox{gyrogroups} whose operations are, in some sense, most far from being associative called contra-associative gyrogroups. The other family consists of gyrogroups that are, in some sense, most close to groups called g-extensive gyrogroups. We then describe their structural properties, which eventually lead to studying the extension problem for gyrogoups in detail using the notion of associators. In particular, we refine the hierarchy of gyrogroup structure by showing that generic gyrogroups are extensions of contra-associative gyrogroups or g-extensive gyrogroups.

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Cite This Article

Suksumran, T. (2025). On the extension problem for gyrogroups. International Electronic Journal of Algebra, Volume: 37 Issue: 37. https://doi.org/10.24330/ieja.1557211

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