Cliff–Weiss inequalities and the Zassenhaus Conjecture

Leo Margolis, Angel Del Rio

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

Let N be a nilpotent normal subgroup of the finite group G. Assume that u is a unit of finite order in the integral group ring ZG of G which maps to the identity under the linear extension of the natural homomorphism G -> G/N. We show how a result of Cliff and Weiss can be used to derive linear inequalities on the partial augmentations of u and apply this to the study of the Zassenhaus Conjecture. This conjecture states that any unit of finite order in ZG is conjugate in the rational group algebra of G to an element in ±G.
Original languageEnglish
Pages (from-to)292-319
Number of pages28
JournalJournal of Algebra
Volume507
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

  • Integral group ring
  • Groups of units
  • Zassenhaus conjecture

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