Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2402.17053

Ideals of some Green biset functors

J. Miguel Calderón
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this article, we describe the lattice of ideals of some Green biset functors. We consider Green biset functors which satisfy that each evaluation is a finite dimensional split semisimple commutative algebra and use the idempotents in these evaluations to characterize any ideal of these Green biset functors. For this we will give the definition of M C-group, this definition generalizes that of a B-group, given for the Burnside functor. Given a Green biset functor A, with the above hypotheses, the set of all M C-groups of A has a structure of a poset and we prove that there exists an isomorphism of lattices between the set of ideals of A and the set of upward closed subsets of the M C-groups of A.

Explore related subjects

math.GR

Keep this discovery

BibTeXRIS

J. Miguel Calderón. 2024-02-26. Ideals of some Green biset functors. https://arxiv.org/abs/2402.17053

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Reversibility and its asymptotic counting in Picard group

We investigate reversible elements in the Picard modular group $\mathrm{PSL}(2,\mathbb{Z}[i])$. We show that reversibility coincides with strong reversibility for Kleinian groups, in particular for the Picard group. We classify reversible elements in the Picard group and characterize loxodromic reversible elements up to conjugacy. We prove that each such conjugacy class contains exactly eight special representatives. We also obtain asymptotic estimates for the number of reversible conjugacy classes with bounded trace.

math.GR↗
arXiv2026

Conjugator length in finitely generated groups

We describe all functions $\mathbb{N}\rightarrow \mathbb{N}$ that can be realized, up to the standard equivalence, as conjugator length functions of finitely generated groups. Furthermore, we show that any two increasing functions $f,g\colon \mathbb N\to \mathbb N$ can be simultaneously realized as conjugator length functions of finitely generated, commensurable (in particular, quasi-isometric) groups.

math.GR↗
arXiv2026

The spectrum of conjugator length functions

A recent program tries to find which functions appear as conjugator length functions. In this note, we show that any (computable) increasing function larger than $n$ appears as $\mathrm{Cl}_G$ for some finitely generated (recursively presented) group. On the other hand, we demonstrate that either $\mathrm{Cl}_G$ must be constant or $\mathrm{Cl}_G(n)\succ n$. Combining these, we obtain a complete description of which functions appear as conjugator length functions of finitely generated groups.

math.GR↗