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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Finite automorphic algebras over $\textrm {GF}(2)$
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by Fletcher Gross PDF
Proc. Amer. Math. Soc. 31 (1972), 10-14 Request permission

Abstract:

If $A$ is a finite nonassociative algebra over ${\text {GF}}(2)$ and $G$ is a group of automorphisms of $A$ such that $G$ transitively permutes the nonzero elements of $A$, then it is shown that either ${A^2} = 0$ or the nonzero elements of $A$ form a quasi-group under multiplication. Under the additional hypothesis that $G$ is solvable, the algebra $A$ is completely determined.
References
Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 31 (1972), 10-14
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0286856-7
  • MathSciNet review: 0286856