Babai's conjecture for high-rank classical groups with random generators
| Autor: | Sean Eberhard, Urban Jezernik |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Classical group
Conjecture Cayley graph General Mathematics 010102 general mathematics 0102 computer and information sciences Group Theory (math.GR) 01 natural sciences Prime (order theory) Combinatorics 010201 computation theory & mathematics Bounded function 20F69 20G40 20P05 05C80 05C81 05C25 20D06 51N30 FOS: Mathematics Rank (graph theory) Mathematics - Combinatorics Combinatorics (math.CO) 0101 mathematics Mathematics - Group Theory Mathematics |
| Popis: | Let $G = \mathrm{SCl}_n(q)$ be a quasisimple classical group with $n$ large, and let $x_1, \dots, x_k \in G$ random, where $k \geq q^C$. We show that the diameter of the resulting Cayley graph is bounded by $q^2 n^{O(1)}$ with probability $1 - o(1)$. In the particular case $G = \mathrm{SL}_n(p)$ with $p$ a prime of bounded size, we show that the same holds for $k = 3$. 44 pages. Several typos corrected. Referee comments incorporated |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|