Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Is a semidirect product of groups necessarily a group?

Authors: Gary F. Birkenmeier, C. Brad Davis, Kevin J. Reeves and Sihai Xiao
Journal: Proc. Amer. Math. Soc. 118 (1993), 689-692
MSC: Primary 20N05; Secondary 20E22
MathSciNet review: 1157998
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The aim of this paper is to provide nonassociative commutative loops which are semidirect products of subgroups.

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

  • [1] A. A. Albert, On Jordan algebras of linear transformations, Trans. Amer. Math. Soc. 59 (1946), 524-555. MR 0016759 (8:63c)
  • [2] R. H. Bruck, Contributions of the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245-354. MR 0017288 (8:134b)
  • [3] -, What is a loop? (A. A. Albert, ed.) MAA Stud. Math., vol. 2, Math. Assoc. Amer., Washington, DC, 1963.
  • [4] -, A survey of binary systems, third printing, Springer-Verlag, New York, 1971.
  • [5] O. Chein, Moufang loops of small order. I, Trans. Amer. Math. Soc. 188 (1974), 31-51. MR 0330336 (48:8673)
  • [6] N. Jacobson, Basic algebra. I, Freeman, San Francisco, CA, 1974. MR 0356989 (50:9457)
  • [7] -, Basic algebra. II, Freeman, San Francisco, CA, 1980. MR 571884 (81g:00001)
  • [8] I. Niven and H. S. Zuckerman, An introduction to the theory of numbers, second printing, Wiley, New York, 1962.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20N05, 20E22

Retrieve articles in all journals with MSC: 20N05, 20E22

Additional Information

Keywords: Loop, group, semidirect product, nucleus, field
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society