Intersection-saturated groups without free subgroups
Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 637-645
Voir la notice de l'article provenant de la source EMS Press
A group G is said to be intersection-saturated if for every strictly positive integer n and every map c:P({1,...,n})∖∅→{0,1}, one can find subgroups H1,...,Hn≤G such that for every non-empty subset I⊆{1,...,n}, the intersection ⋂i∈IHi is finitely generated if and only if c(I)=0. We obtain a new criterion for a group to be intersection-saturated based on the existence of arbitrarily high direct powers of a subgroup admitting an automorphism with a non-finitely generated set of fixed points. We use this criterion to find new examples of intersection-saturated groups, including Thompson’s groups and the Grigorchuk group. In particular, this proves the existence of finitely presented intersection-saturated groups without non-abelian free subgroups, thus answering a question of Delgado, Roy and Ventura.
Classification :
20E07
Mots-clés : intersection-saturated groups, Thompson’s groups, Grigorchuk group, branch groups
Mots-clés : intersection-saturated groups, Thompson’s groups, Grigorchuk group, branch groups
Affiliations des auteurs :
Dominik Francoeur 1
Dominik Francoeur. Intersection-saturated groups without free subgroups. Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 637-645. doi: 10.4171/ggd/891
@article{10_4171_ggd_891,
author = {Dominik Francoeur},
title = {Intersection-saturated groups without free subgroups},
journal = {Groups, geometry, and dynamics},
pages = {637--645},
year = {2025},
volume = {19},
number = {2},
doi = {10.4171/ggd/891},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/891/}
}
Cité par Sources :