Diameters of random Cayley graphs of finite nilpotent groups
| Autor: | Daniel El-Baz, Carlo Pagano |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
Cayley graph 010102 general mathematics Probability (math.PR) Group Theory (math.GR) 01 natural sciences 010101 applied mathematics Combinatorics Nilpotent Mathematics::Group Theory Unimodular matrix Bounded function FOS: Mathematics Rank (graph theory) Mathematics - Combinatorics Combinatorics (math.CO) 0101 mathematics Nilpotent group Abelian group Mathematics - Group Theory Group theory Mathematics - Probability Mathematics |
| Zdroj: | Journal of Group Theory |
| Popis: | We prove the existence of a limiting distribution for the appropriately rescaled diameters of random undirected Cayley graphs of finite nilpotent groups of bounded rank and nilpotency class, thus extending a result of Shapira and Zuck which dealt with the case of abelian groups. The limiting distribution is defined on a space of unimodular lattices, as in the case of random Cayley graphs of abelian groups. Our result, when specialised to a certain family of unitriangular groups, establishes a very recent conjecture of Hermon and Thomas. We derive this as a consequence of a general inequality, showing that the diameter of a Cayley graph of a nilpotent group is governed by the diameter of its abelianisation. Comment: 8 pages |
| Databáze: | OpenAIRE |
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