From examples to methods: Two cases from the study of units in integral group rings

Autor:	Bächle, Andreas, Margolis, Leo
Rok vydání:	2020
Předmět:	Mathematics - Rings and Algebras Mathematics - Group Theory Mathematics - Representation Theory 16U60 (Primary) 20C05 20C15 20C20 (Secondary)
Druh dokumentu:	Working Paper
Popis:	In this article, we review the proofs of the first Zassenhaus Conjecture on conjugacy of torsion units in integral group rings for the alternating groups of degree 5 and 6, by Luthar-Passi and Hertweck. We describe how the study of these examples led to the development of two methods -- the HeLP method and the lattice method. We exhibit these methods and summarize some results which were achieved using them. We then apply these methods to the study of the first Zassenhaus conjecture for the alternating group of degree 7 where only one critical case remains open for a full answer. Along the way we show in examples how recently obtained results can be combined with the methods presented and collect open problems some of which could be attacked using these methods. Comment: To appear in a special volume on the topics of the academic activity at Group Algebras, Representations and Computation 2019 held at the ICTS Bangalore. 18 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.09031 Zobrazit plný text záznamu View this record from Arxiv