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arXiv · 2606.25180

Transfer systems give matroids only for cyclic $p$-groups

Yuri J. F. Sulyma
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Abstract

Transfer systems as studied in equivariant algebra admit minimal generating sets, analogous to bases in linear algebra. It is natural to wonder if minimal generating sets form a matroid. We show that this happens only for lattices which are linear orders, or for cyclic groups of prime power order. In this case, we compute some invariants of the resulting matroid.

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Yuri J. F. Sulyma. 2026-06-23. Transfer systems give matroids only for cyclic $p$-groups. https://arxiv.org/abs/2606.25180

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