Pacific Journal of Mathematics

Combinatorial structures in loops. II. Commutative inverse property cyclic neofields of prime-power order.

E. C. Johnsen and Thomas Storer

Article information

Source
Pacific J. Math. Volume 52, Number 1 (1974), 115-127.

Dates
First available: 8 December 2004

Permanent link to this document
http://projecteuclid.org/euclid.pjm/1102912218

Zentralblatt MATH identifier
0286.05007

Zentralblatt MATH identifier
0256.05008

Mathematical Reviews number (MathSciNet)
MR0409222

Subjects
Primary: 05B10: Difference sets (number-theoretic, group-theoretic, etc.) [See also 11B13]
Secondary: 12K05: Near-fields [See also 16Y30]

Citation

Johnsen, E. C.; Storer, Thomas. Combinatorial structures in loops. II. Commutative inverse property cyclic neofields of prime-power order. Pacific Journal of Mathematics 52 (1974), no. 1, 115--127. http://projecteuclid.org/euclid.pjm/1102912218.


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References

  • [1] E. F. Assmus, Jr. and H. F. Mattson, On the number of inequivalent Steinertriple systems, J. Combinatorial Theory, 1 (1966), 301-305; Errata, 2 (1967), 394.
  • [2] R. H. Bruck, What is a loop, in Studies in Modern Algebra (M. A. A. Studies in Mathematics, 2), Prentice-Hall, Inc., Englewood Cliffs, N. J., (1963), 59-99.
  • [3] Jean Doyen, Sur la croissance du nombre de systemes triples de Steiner non iso- morphes, J. Combinatorial Theory, 8 (1970), 424-441.
  • [4] D. R. Hughes, Planar division neo-rings, Trans. Amer. Math. Soc, 80 (1955), 502- 527.
  • [5] E. C. Johnsen and Thomas Storer, Combinatorial structures in loops III.Difference sets in special cyclic neofields, J. Number Theory, to appear.
  • [6] Emma Lehmer, On residue difference sets, Canad. J. Math., 5 (1953), 425-432.
  • [7] Lowell J. Paige, Neofields, Duke Math. J., 16 (1949), 39-60.
  • [8] Rose Peltesohn, Eine Lb'sung der beiden HeffterschenDifferenzenprobieme,Com- positio Math., 6 (1939), 251-257.
  • [9] Thomas Storer, Cyclotomy and Difference Sets, Markham Publishing Co., Chicago, 1967.

See also

  • : E. C. Johnsen, Thomas Storer. Combinatorial structures in loops. I. Elements of the decomposition theory. I [MR 46 #8861] J. Combinatorial Theory Ser. A 14 1973 149--166.
  • : Combinatorial structures in loops. III J. Number Theory, to appear.
  • : Eugene C. Johnsen, Thomas Storer. Combinatorial structures in loops. {IV}. Steiner triple systems in neofields. IV [MR 56 #5319] Math. Z. 138 1974 1--14.