Multiplicative Jordan decomposition in group rings and p-groups with all noncyclic subgroups normal

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3 Citations (Scopus)


Let p be a prime and let G be a finite p-group. We show that if the integral group ring Z[G] satisfies the multiplicative Jordan decomposition property, then every noncyclic subgroup of G is normal. This is used to simplify the work of Hales, Passi and Wilson on the classification of integral group rings of finite 2-groups with the multiplicative Jordan decomposition property.

Original languageEnglish
Pages (from-to)300-313
Number of pages14
JournalJournal of Algebra
Publication statusPublished - 2012 Sep 4



  • 2-Group
  • Integral group rings
  • Jordan decomposition
  • Nilpotent element
  • Noncyclic subgroup
  • P-Group
  • Semisimple element
  • Unit group

ASJC Scopus subject areas

  • Algebra and Number Theory

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