A counterexample to the first Zassenhaus conjecture

Leo Margolis, Florian Eisele

Onderzoeksoutput: Articlepeer review

14 Citaten (Scopus)


Hans J. Zassenhaus conjectured that for any unit u of finite order in the integral group ring of a finite group G there exists a unit a in the rational group algebra of G such that a −1⋅u⋅a=±g for some g∈G. We disprove this conjecture by first proving general results that help identify counterexamples and then providing an infinite number of examples where these results apply. Our smallest example is a metabelian group of order 2 7⋅3 2⋅5⋅7 2⋅19 2 whose integral group ring contains a unit of order 7⋅19 which, in the rational group algebra, is not conjugate to any element of the form ±g.

Originele taal-2English
Pagina's (van-tot)599-641
Aantal pagina's43
TijdschriftAdvances in Mathematics
StatusPublished - 1 dec 2018


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