Finitely generated subgroups of branch groups and subdirect products of just infinite groups

Autor: Rostislav Grigorchuk, Paul-Henry Leemann, Tatiana Nagnibeda

Publikováno v: Izvestiya: Mathematics. 85:1128-1145

The aim of this paper is to describe the structure of the finitely generated subgroups of a family of branch groups, which includes the first Grigorchuk group and the Gupta-Sidki 3-group. This description is made via the notion of block subgroup. We

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::996c88d935e52de5536b3c0f38183d82
https://doi.org/10.1070/im9101

Cayley graphs with few automorphisms

Autor: Paul-Henry Leemann, Mikael De la Salle

Publikováno v: Journal of Algebraic Combinatorics
Journal of Algebraic Combinatorics, 2020, ⟨10.1007/s10801-020-00956-1⟩
Journal of Algebraic Combinatorics, Springer Verlag, 2020, ⟨10.1007/s10801-020-00956-1⟩

We show that every finitely generated group G with an element of order at least $(5rank(G))^{12}$ admits a locally finite directed Cayley graph with automorphism group equal to G. If moreover G is not generalized dihedral, then the above Cayley direc

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2e19deffb61aa55a20b944ebff18b513
https://doi.org/10.1007/s10801-020-00956-1

Cayley graphs with few automorphisms: the case of infinite groups

Autor: Paul-Henry Leemann, Mikael de la Salle

We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relies on random walk techniques. As a consequence, every finitely generate

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0d0102debbebfc865cc7b06db2e046c3
https://hal.archives-ouvertes.fr/hal-02967126

Schreier graphs: transitivity and coverings

Autor: Paul-Henry Leemann

Publikováno v: International Journal of Algebra and Computation

We give a characterization of isomorphisms between Schreier graphs in terms of the groups, subgroups and generating systems. This characterization may be thought as a graph analog of Mostow's rigidity theorem for hyperbolic manifolds. This allows us

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4576856bb3417c2ae905a25d00b1055f
http://arxiv.org/abs/1505.03433