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Investigating transversals as generating sets for groups

2019/12/05 by Maurice Chiodo, Chiodo, Maurice, Robert Crumplin +5
Engineering · Mathematics · #20E99 #20F05 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Rings, Modules, and Algebras #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1912.02717

openalex publication_date 2019/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [3] is was shown that for any group G whose rank (i.e., minimal number of generators) is at most 3, and any finite index subgroup H≤ G with index [G:H]≥ rank(G), one can always find a left-right transversal of H which generates G. In this paper we extend this result to groups of rank at most 4. We also extend this to groups G of arbitrary (finite) rank r provided all the non-trivial divisors of [G:coreG(H)] are at least 2r-1. Finally, we extend this to groups G of arbitrary (finite) rank provided H is malnormal in G.

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