Let G be a finite permutation group on Ω. An ordered sequence (ω1…,ωℓ) of elements of Ω is an irredundant base for G if the pointwise stabilizer is trivial and no point is fixed by the stabilizer of its predecessors. The minimal cardinality of an irredundant base is said to be the base size of G. If all irredundant bases of G have the same cardinality, G is said to be an IBIS group. In this paper, we classify the finite almost simple primitive IBIS groups whose base size is at least 6.
Mastrogiacomo, F., Spiga, P. (2025). IBIS primitive groups of almost simple type. JOURNAL OF ALGEBRA, 670(15 May 2025), 48-103 [10.1016/j.jalgebra.2025.01.026].
IBIS primitive groups of almost simple type
Mastrogiacomo F.;Spiga P.
2025
Abstract
Let G be a finite permutation group on Ω. An ordered sequence (ω1…,ωℓ) of elements of Ω is an irredundant base for G if the pointwise stabilizer is trivial and no point is fixed by the stabilizer of its predecessors. The minimal cardinality of an irredundant base is said to be the base size of G. If all irredundant bases of G have the same cardinality, G is said to be an IBIS group. In this paper, we classify the finite almost simple primitive IBIS groups whose base size is at least 6.
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