Partial groups, pregroups and realisability of fusion systems - Archive ouverte HAL
Article Dans Une Revue Journal of Algebra Année : 2023

Partial groups, pregroups and realisability of fusion systems

Groupes partiels, prégroupes et réalisabilité des systèmes de fusion

Nicolas Lemoine
  • Fonction : Auteur
Rémi Molinier

Résumé

In this article, we compare two different notions of partially defined group strutures, namely partial groups and pregroups, as introduced by Chermak and Stallings respectively. In particular we prove that the category of pregroups can be seen as a full subcategory of the category of partial groups. We also bring out some conjugation properties about elements and subgroups of finite order in pregroups and their universal groups. We then use these to investigate the question of realisability of fusion systems in finite pregroups.
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Dates et versions

hal-04008275 , version 1 (09-03-2023)
hal-04008275 , version 2 (04-09-2024)

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Nicolas Lemoine, Rémi Molinier. Partial groups, pregroups and realisability of fusion systems. Journal of Algebra, 2023. ⟨hal-04008275v2⟩
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