Partial augmentations power property: A Zassenhaus Conjecture related problem

Leo Margolis, Angel Del Rio

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Zassenhaus conjectured that any unit of finite order in the integral group ring 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

, 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.
Original languageEnglish
Pages (from-to)4089-4101
Number of pages13
JournalJournal of Pure and Applied Algebra
Volume223
Issue number9
DOIs
Publication statusPublished - Sep 2019

Keywords

  • Groups of units
  • Integral group ring
  • Partial augmentation
  • Zassenhaus Conjecture

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