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- W2765147274 abstract "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 $a^{-1}cdot u cdot a=pm g$ for some $gin G$. 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 $2^7 cdot 3^2 cdot 5 cdot 7^2 cdot 19^2$ whose integral group ring contains a unit of order $7 cdot 19$ which, in the rational group algebra, is not conjugate to any element of the form $pm g$." @default.
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- W2765147274 date "2017-10-24" @default.
- W2765147274 modified "2023-09-27" @default.
- W2765147274 title "A Counterexample to the First Zassenhaus Conjecture" @default.
- W2765147274 hasPublicationYear "2017" @default.
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