有限基元群非冗余基的枢轴性

arXiv - MATH - Group Theory Pub Date : 2024-07-30 DOI:arxiv-2407.20849

Fabio Mastrogiacomo

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引用次数: 0

摘要

让 $G$ 是作用于集合 $\Omega$ 的有限置换群。如果$\Omega$元素的有序序列$(\omega_1,\ldots,\omega_\ell)$的点稳定器是微不足道的，并且没有点被其前序的稳定器固定，那么这个序列就是$G$的冗余基。我们证明，自然数的任何区间都可以实现为某个有限基元群的冗基的心数集。

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Cardinalities of irredundant bases of finite primitive groups

Let $G$ be a finite permutation group acting on a set $\Omega$. An ordered sequence $(\omega_1,\ldots,\omega_\ell)$ of elements of $\Omega$ is an irredundant base for $G$ if the pointwise stabilizer of the sequence is trivial and no point is fixed by the stabilizer of its predecessors. We show that any interval of natural numbers can be realized as the set of cardinalities of irredundant bases for some finite primitive group.

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arXiv - MATH - Group Theory

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