We study the planar 3-colorable subgroup E of Thompson’s group F and its even part ϵEVEN. The latter is obtained by cutting E with a finite index subgroup of F isomorphic to F, namely the rectangular subgroup K(2,2). We show that the even part ϵEVEN of the planar 3-colorable subgroup admits a description in terms of stabilisers of suitable subsets of dyadic rationals. As a consequence ϵEVEN is closed in the sense of Golan and Sapir. We then study three quasi-regular representations associated with ϵEVEN: two are shown to be irreducible and one to be reducible.
THE PLANAR 3-COLORABLE SUBGROUP E OF THOMPSON’S GROUP F AND ITS EVEN PART / Aiello, V.; Nagnibeda, T.. - In: PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY. - ISSN 0013-0915. - 68:1(2024), pp. 173-197. [10.1017/S0013091524000452]
THE PLANAR 3-COLORABLE SUBGROUP E OF THOMPSON’S GROUP F AND ITS EVEN PART
Aiello V.
;
2024
Abstract
We study the planar 3-colorable subgroup E of Thompson’s group F and its even part ϵEVEN. The latter is obtained by cutting E with a finite index subgroup of F isomorphic to F, namely the rectangular subgroup K(2,2). We show that the even part ϵEVEN of the planar 3-colorable subgroup admits a description in terms of stabilisers of suitable subsets of dyadic rationals. As a consequence ϵEVEN is closed in the sense of Golan and Sapir. We then study three quasi-regular representations associated with ϵEVEN: two are shown to be irreducible and one to be reducible.| File | Dimensione | Formato | |
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