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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Groups of square-free order, an algorithm


Author: J. Alonso
Journal: Math. Comp. 30 (1976), 632-637
MSC: Primary 20D99; Secondary 20-04
MathSciNet review: 0506898
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Abstract: An abstract definition of the groups of square-free order is given that leads naturally to a programmable computation of their number. O. Hölder's alternative description of the groups of square-free order is incidentally derived.


References [Enhancements On Off] (What's this?)

  • [1] O. HÖLDER, "Die Gruppen der Ordnung $ {p^3},p{q^2},pqr,{p^4}$," Math. Ann., v. 43, 1893, pp. 300-412.
  • [2] O. HÖLDER, "Die gruppen mit quadratfreier Ordnungzahl", Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Kl., v. 1895, pp. 211-229.
  • [3] W. R. Scott, Group theory, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0167513 (29 #4785)
  • [4] Saunders Mac Lane and Garrett Birkhoff, Algebra, The Macmillan Co., New York; Collier-Macmillan Ltd., London, 1967. MR 0214415 (35 #5266)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1976-0506898-5
PII: S 0025-5718(1976)0506898-5
Article copyright: © Copyright 1976 American Mathematical Society