Hopfian combinatorial wreath products
Dessislava H. Kochloukova

TL;DR
This paper investigates conditions under which combinatorial wreath products of abelian groups are Hopfian, providing new examples and characterizations of automorphism groups in this context.
Contribution
It generalizes previous results on Hopfian properties of wreath products and offers new examples and automorphism group descriptions under specific conditions.
Findings
Identifies sufficient conditions for wreath products to be Hopfian.
Provides an example where the wreath product is not Hopfian despite the factors being Hopfian.
Describes automorphism groups of wreath products with certain restrictions.
Abstract
Let be an abelian group. We consider sufficient conditions for the combinatorial wreath product to be Hopfian generalising results of Bradford and Fournier-Facio. For an integer we show an example where is not Hopfian but is Hopfian. We describe under some restrictions on , and .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Limits and Structures in Graph Theory · graph theory and CDMA systems
