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arXiv · 2212.13219

IBIS soluble linear groups

Andrea Lucchini·Dmitry Malinin
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Abstract

Let $G$ be a finite permutation group on $\Omega.$ An ordered sequence $(\omega_1,\dots, \omega_t)$ of elements of $\Omega$ is an irredundant base for $G$ if the pointwise stabilizer is trivial and no point is fixed by the stabilizer of its predecessors. If all irredundant bases of $G$ have the same cardinality, $G$ is said to be an IBIS group. In this paper we give a classification of quasi-primitive soluble irreducible IBIS linear groups, and we also describe nilpotent and metacyclic IBIS linear groups and IBIS linear groups of odd order.

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Andrea Lucchini, Dmitry Malinin. 2022-12-26. IBIS soluble linear groups. https://arxiv.org/abs/2212.13219

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