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On the Torsion Units of Some Integral Group Rings

2006; World Scientific; Volume: 13; Issue: 02 Linguagem: Inglês

10.1142/s1005386706000290

1005-3867

Martin Hertweck,

Coding theory and cryptography

Algebra ColloquiumVol. 13, No. 02, pp. 329-348 (2006) No AccessOn the Torsion Units of Some Integral Group RingsMartin HertweckMartin HertweckUniversität Stuttgart, Fachbereich Mathematik, Institut für Geometrie und Topologie, Pfaffenwaldring 57, D-70550 Stuttgart, Germanyhttps://doi.org/10.1142/S1005386706000290Cited by:36 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail AbstractIt is shown that any torsion unit of the integral group ring ℤG of a finite group G is rationally conjugate to a trivial unit if G = P ⋊ A with P a normal Sylow p-subgroup of G and A an abelian p′-group (thus confirming a conjecture of Zassenhaus for this particular class of groups). The proof is an application of a fundamental result of Weiss. 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