Bass-Serre theory and counting rank two amalgams
Rieuwert J. Blok, Corneliu Hoffman
TL;DR
This paper extends Bass-Serre theory to classify all possible rank two amalgams of groups, providing a systematic approach to understanding complex subgroup structures within larger groups.
Contribution
It generalizes previous classifications of Curtis-Tits shape amalgams to all rank two amalgams using Bass-Serre theory.
Findings
Classified all rank two amalgams using Bass-Serre theory
Provided a method to determine largest groups containing given amalgam structures
Extended previous work on Curtis-Tits shape amalgams
Abstract
An amalgam of groups can be viewed as a Sudoku game inside a group. You are given a set of subgroups and their intersections and you need to decide what the largest group containing such a structure can be. In a recent paper (0907.1388v1) we used Bass-Serre theory of graphs of groups to classify all possible amalgams of Curtis-Tits shape with a given diagram. This note describes the method for general rank two amalgams.
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
Topicsgraph theory and CDMA systems · Finite Group Theory Research · Coding theory and cryptography