We prove that if G is a finite primitive permutation group and if g is an element of G, then either g has a cycle of length equal to its order, or for some r, m and k, the group G ≤ Sym(m)wrSym(r) preserves the product structure of r direct copies of the natural action of Sym(m) on k-sets. This gives an answer to a question of Siemons and Zalesski and a solution to a conjecture of Giudici, Praeger and the second author.
Guest, S., Spiga, P. (2017). Finite primitive groups and regular orbits of group elements. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 369(2), 997-1024 [10.1090/tran6678].
Finite primitive groups and regular orbits of group elements
SPIGA, PABLO
2017
Abstract
We prove that if G is a finite primitive permutation group and if g is an element of G, then either g has a cycle of length equal to its order, or for some r, m and k, the group G ≤ Sym(m)wrSym(r) preserves the product structure of r direct copies of the natural action of Sym(m) on k-sets. This gives an answer to a question of Siemons and Zalesski and a solution to a conjecture of Giudici, Praeger and the second author.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
S0002-9947-2016-06678-7.pdf
Solo gestori archivio
Tipologia di allegato:
Author’s Accepted Manuscript, AAM (Post-print)
Dimensione
421.49 kB
Formato
Adobe PDF
|
421.49 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
