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

On the extension problem for gyrogroups

Teerapong Suksumran(Chiang Mai University)
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Yayın Tarihi
2025-01-14
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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 Maddede Bu Makale

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Amaç & Hipotez:A gyrogroup is an algebraic structure whose operation is in \mbox{general} non-associative and shares common properties with groups.
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Temel Bulgular & Veri:In this paper, we introduce two disjoint families of gyrogroups.
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Sonuç & Katkı:In particular, we refine the hierarchy of gyrogroup structure by showing that generic gyrogroups are extensions of contra-associative gyrogroups or g-extensive gyrogroups.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (19)

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