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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The structure of conjugacy closed loops
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by Kenneth Kunen PDF
Trans. Amer. Math. Soc. 352 (2000), 2889-2911 Request permission

Abstract:

We study structure theorems for the conjugacy closed (CC-) loops, a specific variety of G-loops (loops isomorphic to all their loop isotopes). These theorems give a description all such loops of small order. For example, if $p$ and $q$ are primes, $p < q$, and $q-1$ is not divisible by $p$, then the only CC-loop of order $pq$ is the cyclic group of order $pq$. For any prime $q > 2$, there is exactly one non-group CC-loop in order $2q$, and there are exactly three in order $q^2$. We also derive a number of equations valid in all CC-loops. By contrast, every equation valid in all G-loops is valid in all loops.
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Additional Information
  • Kenneth Kunen
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • MR Author ID: 107920
  • Email: kunen@math.wisc.edu
  • Received by editor(s): September 27, 1996
  • Received by editor(s) in revised form: March 13, 1998
  • Published electronically: February 16, 2000
  • Additional Notes: Author supported by NSF Grants CCR-9503445 and DMS-9704520. The author is grateful to the referee for many helpful comments on the original draft of this paper.
  • © Copyright 2000 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 2889-2911
  • MSC (2000): Primary 20N05; Secondary 03C05, 08A05
  • DOI: https://doi.org/10.1090/S0002-9947-00-02350-3
  • MathSciNet review: 1615991