Uniformly semi-rational simple groups
Marco Vergani

TL;DR
This paper classifies non-abelian simple groups, especially alternating groups, that have a uniform semi-rational property related to the conjugacy classes of their cyclic subgroups' generators.
Contribution
It provides a classification of uniformly semi-rational non-abelian simple groups, focusing on the structure of their conjugacy classes, particularly in alternating groups.
Findings
Identifies conditions under which simple groups are uniformly semi-rational.
Classifies all such groups among non-abelian simple groups.
Highlights the special case of alternating groups.
Abstract
A finite group is called uniformly semi-rational if there exists an integer such that the generators of every cyclic sugroup of lie in at most two conjugacy classes, namely or . In this paper, we provide a classification of uniformly semi-rational non-abelian simple groups with particular focus on alternating groups.
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 Topics in Algebra · Functional Equations Stability Results · Geometric and Algebraic Topology
