2017/06/15 by Leo Margolis, Ángel del Río, Ángel del Rı́o +2 · 1 citation
Computer Science · Engineering · Mathematics · #16S34 #16U60 #20C05 #20C10 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #graph theory and CDMA systems #math.GR #math.RA #math.RT #msc:16S34 #msc:16U60 #msc:20C05 #msc:20C10
paper · pdf · doi:10.48550/arxiv.1706.04787
14 pages. A gap fixed and some typos corrected
openalex publication_date 2017/06/15 · arxiv created 2018/11/02 · arxiv updated 2018/11/05 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Zassenhaus conjectured that any unit of finite order in the integral group ring ℤG of a finite group G is conjugate in the rational group algebra of G to an element in ± G. We review the known weaker versions of this conjecture and introduce a new condition, on the partial augmentations of the powers of a unit of finite order in ℤG, which is weaker than the Zassenhaus Conjecture but stronger than its other weaker versions. We prove that this condition is satisfied for units mapping to the identity modulo a nilpotent normal subgroup of G. Moreover, we show that if the condition holds then the HeLP Method adopts a more friendly form and use this to prove the Zassenhaus Conjecture for a special class of groups.