REVIEW 3 cited by
Conjugacy growth series of some wreath products
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
Signed reviews
abstract
In this paper we consider groups of the form $G\wr L$, where the set of generators naturally extends the sets of generators of $G$ and $L$, and $L$ admits a Cayley graph that is a tree. We show how one can compute the conjugacy growth series of such groups in terms of the standard and conjugacy growth series of $G$. We then provide explicit formulas for groups of the form $G\wr \mathbb{Z}$ and $G\wr (C_2*C_2)$. We also prove that the radius of convergence of the conjugacy growth series of $G\wr L$, for any $G$ and $L$ as above, is the same as the radius of convergence of its standard growth series.
Forward citations
Cited by 3 Pith papers
-
On finite extensions of lamplighter groups
A single family of finite extensions of lamplighter groups separates uniform from non-uniform subgroup membership, pairs rational growth with an undecidable word problem, and pairs a context-free conjugacy geodesic la...
-
Contracting elements and conjugacy growth in Coxeter groups, graph products, and further groups
Periagroups that are infinite and not virtually direct products contain contracting elements in their standard Cayley graphs, implying acylindrical hyperbolicity and transcendental conjugacy growth series.
-
The conjugacy growth of the soluble Baumslag-Solitar groups
For each k at least 2, the conjugacy growth series of BS(1,k) with respect to the standard generating set is transcendental, and its growth rate equals the standard growth rate.
Discussion (0). Continue with ORCID to comment.