A well-known conjecture of Babai states that if G is any finite simple group and X is a generating set for G, then the diameter of the Cayley graph Cay(G, X) is bounded by log ∣G∣c for some universal constant c. In this paper, we prove such a bound for Cay(G, X) for G = PSL(n, q), PSp(n, q) or PSU(n, q) where q is odd, under the assumptions that X contains a transvection and q ≠ 9 or 81.
On the diameter of Cayley graphs of classical groups with generating sets containing a transvection
Garonzi, MartinoPrimo
;
2024
Abstract
A well-known conjecture of Babai states that if G is any finite simple group and X is a generating set for G, then the diameter of the Cayley graph Cay(G, X) is bounded by log ∣G∣c for some universal constant c. In this paper, we prove such a bound for Cay(G, X) for G = PSL(n, q), PSp(n, q) or PSU(n, q) where q is odd, under the assumptions that X contains a transvection and q ≠ 9 or 81.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
28_Paper_Babai_Conjecture_Published_Version_ISRAEL.pdf
accesso aperto
Descrizione: versione editoriale
Tipologia:
Full text (versione editoriale)
Licenza:
Creative commons
Dimensione
389.42 kB
Formato
Adobe PDF
|
389.42 kB | Adobe PDF | Visualizza/Apri |
I documenti in SFERA sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
