Uniqueness of roots up to conjugacy in circular and hosohedral-type Garside groups
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Owen Garnier
Abstract
We consider a particular class of Garside groups, which we call circular groups. We mainly prove that roots are unique up to conjugacy in circular groups. This allows us to completely classify these groups up to isomorphism. As a consequence, we obtain the uniqueness of roots up to conjugacy in complex braid groups of rank 2. We also consider a generalization of circular groups, called hosohedral-type groups. These groups are defined using circular groups, and a procedure called the Δ-product, which we study in generality. We also study the uniqueness of roots up to conjugacy in hosohedral-type groups.
Acknowledgements
This work is part of my PhD thesis, done under the supervision of Pr. Ivan Marin. I thank him for his precious advice, especially in Sections 2.3.1 and 2.3.2. I would also like to thank Mireille Soergel and Igor Haladjian for stimulating discussions.
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Communicated by: Olivier Dudas
References
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- Finite normal subgroups of strongly verbally closed groups
- The central tree property and algorithmic problems on subgroups of free groups
- Uniqueness of roots up to conjugacy in circular and hosohedral-type Garside groups
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Articles in the same Issue
- Frontmatter
- The relational complexity of linear groups acting on subspaces
- Cliques in derangement graphs for innately transitive groups
- Representation zeta function of a family of maximal class groups: Non-exceptional primes
- Character degrees of 5-groups of maximal class
- Automorphic word maps and the Amit–Ashurst conjecture
- Groups with subnormal or modular Schmidt 𝑝𝑑-subgroups
- Finite normal subgroups of strongly verbally closed groups
- The central tree property and algorithmic problems on subgroups of free groups
- Uniqueness of roots up to conjugacy in circular and hosohedral-type Garside groups
- Isomorphisms and commensurability of surface Houghton groups
