Let G be a finite permutation group on Ω. An ordered sequence of elements of Ω, (ω1,…,ωt), is an irredundant base for G if the pointwise stabilizer G(ωjavax.xml.bind.JAXBElement@606ca359,…,ωjavax.xml.bind.JAXBElement@77e0dd48) is trivial and no point is fixed by the stabilizer of its predecessors. If all irredundant bases of G have the same size we say that G is an IBIS group. In this paper we show that if a primitive permutation group is IBIS, then it must be almost simple, of affine-type, or of diagonal type. Moreover we prove that a diagonal-type primitive permutation groups is IBIS if and only if it is isomorphic to PSL(2,2f)×PSL(2,2f) for some f≥2, in its diagonal action of degree 2f(22f−1).
Primitive permutation IBIS groups
Lucchini A.
;Morigi M.;Moscatiello M.
2021
Abstract
Let G be a finite permutation group on Ω. An ordered sequence of elements of Ω, (ω1,…,ωt), is an irredundant base for G if the pointwise stabilizer G(ωjavax.xml.bind.JAXBElement@606ca359,…,ωjavax.xml.bind.JAXBElement@77e0dd48) is trivial and no point is fixed by the stabilizer of its predecessors. If all irredundant bases of G have the same size we say that G is an IBIS group. In this paper we show that if a primitive permutation group is IBIS, then it must be almost simple, of affine-type, or of diagonal type. Moreover we prove that a diagonal-type primitive permutation groups is IBIS if and only if it is isomorphic to PSL(2,2f)×PSL(2,2f) for some f≥2, in its diagonal action of degree 2f(22f−1).File | Dimensione | Formato | |
---|---|---|---|
2102.12803.pdf
accesso aperto
Tipologia:
Preprint (submitted version)
Licenza:
Accesso libero
Dimensione
212.44 kB
Formato
Adobe PDF
|
212.44 kB | Adobe PDF | Visualizza/Apri |
Pubblicazioni consigliate
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.