aequationes mathematicae

, Volume 44, Issue 1, pp 48–59 | Cite as

Simulated factorizations II

  • A. D. Sands
Research Papers


A factorization of a finite abelian group is said to be simulated if it is obtained from a factorization into a direct product of subgroups by changing at mostk elements in each subgroup. The question has been asked as to which values ofk imply that in fact at least one subgroup must be left unaltered. This has been shown to be true fork = 1 but to be false, in general, fork = p − 1, wherep is the least prime dividing the order ofG. In this paper it is shown to be true fork = p − 2.

AMS (1991) subject classification

Primary 20K01 Secondary 52A45 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Corrádi, K., Sands, A. D. andSzabó, S.,Simulated factorizations. J. Algebra (to appear).Google Scholar
  2. [2]
    Corrádi, K., Szabó, S.,A new proof of Redei's theorem. Pacific J. Math.140 (1989), 53–61.Google Scholar
  3. [3]
    De Bruijn, N. G.,On the factorization of finite abelian groups. Indag. Math.15 (1953), 258–264.Google Scholar
  4. [4]
    Hajós, G.,Über einfache und mehrfache Bedeckung des n-dimensionalen Raumes mit einem Würfelgitter. Math. Z.47 (1942), 427–467.Google Scholar
  5. [5]
    Rédel, L.,Zwei Lückensatze über Polynome in endlichen Primkörpern mit Anwendung auf die endlichen Abelschen Gruppen und die Gaussischen Summen. Acta Math.79 (1947), 273–290.Google Scholar
  6. [6]
    Rédel, L.,Die neue Theorie der endlichen Abelschen Gruppen und Verallgemeinerung des Haupsatzes von Hajós. Acta Math. Acad. Sci. Hung.16 (1965), 329–373.Google Scholar
  7. [7]
    Wittman, E.,Einfacher Beweis des Haupsatzes von Hajós — Rédei für elementare Gruppen von Primzahlquadratordnung. Acta Math. Acad. Sci. Hungar.20 (1969), 227–230.Google Scholar

Copyright information

© Birkhäuser Verlag 1992

Authors and Affiliations

  • A. D. Sands
    • 1
  1. 1.Department of MathematicsThe UniversityDundeeScotland

Personalised recommendations