Random presentations and random subgroups: a survey

Frédérique Bassino (1) , Cyril Nicaud (2) , Pascal Weil (3, 4)

1 LIPN - Laboratoire d'Informatique de Paris-Nord
2 LIGM - Laboratoire d'Informatique Gaspard-Monge
3 LaBRI - Laboratoire Bordelais de Recherche en Informatique
4 ReLaX - Research Lab in Computer Science

This is a survey of results on random group presentations, and on random subgroups of certain fixed groups. Being a survey, this paper does not contain new results, but it offers a synthetic view of a part of this very active field of research.

Domaines: Théorie des groupes [math.GR]

Frédérique Bassino, Cyril Nicaud, Pascal Weil. Random presentations and random subgroups: a survey. Frédérique Bassino, Ilya Kapovich, Markus Lohrey, Alexei Miasnikov, Cyril Nicaud, Andrey Nikolaev, Igor Rivin, Vladimir Shpilrain, Alexander Ushakov and Pascal Weil. Complexity and Randomness in Group Theory - GAGTA Book 1, de Gruyter, 2020, 978-3-11-066491-1. ⟨hal-01456207v2⟩