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Moufang loops of small order

About this Title

Orin Chein

Publication: Memoirs of the American Mathematical Society
Publication Year: 1978; Volume 13, Number 197
ISBNs: 978-0-8218-2197-8 (print); 978-1-4704-0202-0 (online)
DOI: https://doi.org/10.1090/memo/0197
MathSciNet review: 0466391

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Table of Contents

Chapters

  • Introduction
  • I. Background and notation
  • II. Groups and loops of order $\leq 31$
  • III. Some helpful construction theorems
  • IV. Properties of loops satisfying the hypotheses of Theorem 1
  • V. Some results on isomorphism
  • VI. The construction process
  • VII. Loops requiring four or more generators
  • VIII. Three-generator loops of the form $M_{2n}(G,2)$
  • IX. Three-generator loops, not of the form $M_{2n}(G,2)$, which contain an element of order greater than 6
  • X. Three-generator loops which contain an element of order 6 but no element of order greater than 6
  • XI. Three-generator loops which contain an element of order five but no element of larger order
  • XII. Three-generator loops which contain an element of order four but no element of larger order
  • XIII. Three-generator loops containing no element of order greater than three
  • XIV. Summary