Finite Groups with Odd Sylow Normalizers
Robert M. Guralnick, Gabriel Navarro, Pham Huu Tiep
TL;DR
This paper characterizes the structure of finite groups with Sylow normalizers of odd order and proves important conjectures in group theory for these groups.
Contribution
It identifies the non-abelian composition factors of such groups and confirms the McKay and Alperin weight conjectures for them.
Findings
Determined the non-abelian composition factors of the groups.
Proved the McKay conjecture for these groups.
Proved the Alperin weight conjecture for these groups.
Abstract
We determine the non-abelian composition factors of the finite groups with Sylow normalizers of odd order. As a consequence, among others, we prove the McKay conjecture and the Alperin weight conjecture for these 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
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems