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National Academy Science Letters

, Volume 42, Issue 3, pp 245–247 | Cite as

Construction of Right Gyrogroups

  • Akhilesh Chandra YadavEmail author
Short Communication

Abstract

Attempts have been made to introduce notion of class assigned functions k for a given group G and observed that it determines a right gyrogroup \((G, o_k)\). It is also observes that \((G, o_k)\) will be a group if and only if G is a nilpotent group of class 2 and will be a gyrogroup for a nilpotent group of class 3, where \(k(x)=1\) for all \(x\in G\setminus \{1\}\).

Keywords

Right gyrogroups Gyrotransversals Gyrogroups 

Mathematics Subject Classification

20N05 

References

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    Foguel T, Ungar AA (2000) Involutory decomposition of groups into twisted subgroups and subgroups. J Group Theory 3:27–46MathSciNetCrossRefzbMATHGoogle Scholar
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    Lal R (1996) Transversals in groups. J Algebra 181:70–81MathSciNetCrossRefzbMATHGoogle Scholar
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    Lal R, Yadav AC (2013) Topological right gyrogroups and gyrotransversals. Commun Algebra 41(9):3559–3575.  https://doi.org/10.1080/00927872.2012.690467 MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The National Academy of Sciences, India 2018

Authors and Affiliations

  1. 1.Department of MathematicsMahatma Gandhi Kashi VidyapithVaranasiIndia

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