Solvable and Nilpotent Right Loops

2014/02/14 by Vivek Kumar Jain, Jain, Vivek Kumar, Vipul Kakkar +1 · 1 citation
Engineering · Mathematics · #20D60 #20N05 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematics and Applications #graph theory and CDMA systems #math.GR #msc:20D60 #msc:20N05

paper · pdf · doi:10.48550/arxiv.1402.3378

arXiv admin note: substantial text overlap with arXiv:1307.5392

arxiv created 2014/02/14 · openalex publication_date 2014/02/14 · arxiv updated 2014/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper the notion of nilpotent right transversal and solvable right transversal has been defined. Further, it is proved that if a core-free subgroup has a generating solvable transversal or a generating nilpotent transversal, then the whole group is solvable.

Cited by

• A Study of Groups through Transversals

Related

• Invariant transversals in finite groups
• Three concepts of nilpotence in loops
• On torsion-free nilpotent loops
• Formulating basic notions of finite group theory via the lifting\n property
• The R_∞ property for nilpotent quotients of generalized solvable Baumslag-Solitar groups