Primitive permutation IBIS groups

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:184

Article

Lucchini, Andrea¹  Morigi, Marta²  Moscatiello, Mariapia² 

[1] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, I-35121 Padua, Italy

[2] Univ Bologna, Dipartimento Matemat, Piazza Porta San Donato 5, Bologna, Italy

关键词: Primitive group;    Base size;    IBIS group;   

DOI  :  10.1016/j.jcta.2021.105516

来源: Elsevier

【 摘 要 】

Let G be a finite permutation group on Omega. An ordered sequence of elements of Omega, (omega(1), ..., omega(t)), is an irredundant base for G if the pointwise stabilizer G((omega 1, ..., omega t)) 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, 2(f)) x PSL(2, 2(f)) for some f >= 2, in its diagonal action of degree 2(f)(2(2f) - 1). (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free