Archiv der Mathematik

, Volume 85, Issue 3, pp 227–232 | Cite as

Undecidability of the centers of groups and group algebras

  • Yuji Kobayashi
Original Paper


Let k ≧ 3 be an integer or k = ∞ and let K be a field. There is a recursive family \({\left\{ {G_{n} } \right\}}_{{n \in \mathbb{N}}} \) of finitely presented groups G n over a fixed finite alphabet with solvable word problem such that
  1. (1)

    the center of G n is trivial for every \(n \in \mathbb{N},\)

  2. (2)

    the dimension d(n) of the center of the group algebra K · G n over K is either 1 or k, and

  3. (3)

    it is undecidable given n whether d(n) = 1 or d(n) = k.


Mathematics Subject Classification (2000).

Primary 20F10 Secondary 16S34 20C07 


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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of Information ScienceToho UniversityFunabashiJapan

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