Automorphism groups of superextensions of groups
Taras Banakh, Volodymyr Gavrylkiv

TL;DR
This paper explores the structure of superextensions of groups, proving that group isomorphism is equivalent to superextension isomorphism and describing automorphism groups for small groups.
Contribution
It establishes a fundamental link between group isomorphisms and their superextensions, and characterizes automorphism groups for small groups.
Findings
Group isomorphism iff superextension isomorphism
Automorphism groups of superextensions for groups of size ≤ 5
Extension of binary operations to superextensions
Abstract
The superextension of a set consists of all maximal linked families on . Any associative binary operation can be extended to an associative binary operation . In the paper we study isomorphisms of superextensions of groups and prove that two groups are isomorphic if and only if their superextensions are isomorphic. Also we describe the automorphism groups of superextensions of all groups of cardinality .
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
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Advanced Topology and Set Theory
