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_(ω1,...,ωt) 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).

Lucchini A., Morigi M., Moscatiello M. (2021). Primitive permutation IBIS groups. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 184, 1-17 [10.1016/j.jcta.2021.105516].

Primitive permutation IBIS groups

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_(ω1,...,ωt) 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).
2021
Lucchini A., Morigi M., Moscatiello M. (2021). Primitive permutation IBIS groups. JOURNAL OF COMBINATORIAL THEORY. SERIES A, 184, 1-17 [10.1016/j.jcta.2021.105516].
Lucchini A.; Morigi M.; Moscatiello M.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/846160
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