Fusion systems on a Sylow p-subgroup of SU4(p)

Moragues, Raul

doi:10.1016/j.jalgebra.2021.09.019

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Appendix a Gap Algorithms For Fusion-invariant Representations1

Introduction1

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2024

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Cited by 4 publications

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“…Using the algorithms above, we found new examples of non-factorial monoids of the form Rep G (S), which we present in the following table together with the examples from [12] and [23]. We applied them to groups with Sylows of order 2 4 , 2 5 and 3 4 corresponding to the fusion systems in Propositions 4.3 and 4.4 of [1], to some of the fusion systems in Tables 1 and 2 of Chapter 7 of [21], and other classical groups. The column "Irr.…”

Section: Appendix a Gap Algorithms For Fusion-invariant Representationsmentioning

confidence: 99%

Uniqueness of factorization for fusion-invariant representations

Cantarero¹,

Combariza²

2023

Preprint

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Given a saturated fusion system F over a finite p-group S, we provide criteria to determine when uniqueness of factorization into irreducible F -invariant representations holds. We use them to prove uniqueness of factorization when the order of S is at most p 3 . We also describe an example where the monoid of fusioninvariant representations is not even half-factorial. Finally, we find other examples of fusion systems where this monoid is not factorial using GAP.

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Section: Appendix a Gap Algorithms For Fusion-invariant Representationsmentioning

confidence: 99%

Uniqueness of factorization for fusion-invariant representations

Cantarero¹,

Combariza²

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…The case of Sylow p-subgroups of PSU 4 (p), for p an odd prime, was handled disjointly in two papers: the case p = 3 dealt with by Baccanelli, Franchi and Mainardis [BFM19], and the cases p 5 analyzed by Moragues-Moncho [Mon22]. No exotic fusion systems were found here.…”

Section: Introductionmentioning

confidence: 97%