The non-two-primes graph of a finite group

2023/08/31 by Garatea-Zaballa, Karmele, Lucchini, Andrea
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2308.16750

Abstract

To any finite group G, we may associate a graph whose vertices are the elements of G and where two distinct vertices x and y are adjacent if and only if the order of the subgroup ⟨ x, y⟩ is divisible by at least 3 distinct primes. We prove that the subgraph of this graph induced by the non-isolated vertices is connected and has diameter at most 5.

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