Generating hypergraphs of finite groups

Andrea Lucchini

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arXiv · 2404.11186

Generating hypergraphs of finite groups

Andrea Lucchini

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Abstract

In a recent paper Cameron, Lakshmanan and Ajith began an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this can add a new perspective. Following their suggestions, we consider suitable hypergraphs encoding the generating properties of a finite group. In particular, answering a question asked in their paper, we classified the finite solvable groups whose generating hypergraph is the basis hypergraph of a matroid.

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Andrea Lucchini. 2024-04-17. Generating hypergraphs of finite groups. https://arxiv.org/abs/2404.11186

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