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Lander’s Tables are Complete!

  • Joel E. Iiams
Part of the NATO Science Series book series (ASIC, volume 542)

Abstract

In 1983 E.S. Lander published “Symmetric Designs: An Algebraic Approach”. At the back are provided a set of tables. Each entry in a table specifies an abelian group G, the parameters of a putative difference set D in G with cardinality k, whether D exists or not, a construction when D does exist, and a nonexistence proof when D does not exist. At time of publication there were some 25 entries which were open, i.e. the existence or nonexistence of D had not been determined From 1983 until 1993 K.T. Arasu and others filled in all but 8 entries. In 1994 entry 148 was filled in by Hams, Liebler and Smith (1994). In this paper we fill in the last seven entries by demonstrating nonexistence. We point out several applications to nonabelian difference sets.

Keywords

Normal Subgroup Intersection Number Homomorphic Image Starter Block Column Label 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Curtis, C.W. and Reiner, I. (1988) Representation Theory of Finite Groups and Associative Algebras, John Wiley and Sons, New York.zbMATHGoogle Scholar
  2. Iiams, J.E., Liebler, R.A. and Smith, K.W. (1994) Difference sets in nilpotent groups with large Frattini quotient: Geometric methods and (375,34,3) in K.T. Arasu (ed.) Groups, Difference Sets and the Monster, DeGruyter, Berlin-New York, pp.153–163.Google Scholar
  3. Ireland, K. and Rosen, M. (1990) A Classical Introduction to Modern Number Theory, Springer, Berlin-New York.zbMATHGoogle Scholar
  4. Jungnickel, D. and Pott, A. (1999) Difference sets: an introduction, this volumeGoogle Scholar
  5. Lander, E.S. (1983) Symmetric Designs: an Algebraic Approach, London Mathematical Society Lecture Notes Series 74, Cambridge University Press, Cambridge, England.Google Scholar
  6. Liebler, R.A. (1999) Constructive representation theoretic methods and non-Abelian difference sets, this volume.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1999

Authors and Affiliations

  • Joel E. Iiams
    • 1
  1. 1.University of North DakotaGrand ForksUSA

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