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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finite automorphic algebras over $ {\rm GF}(2)$


Author: Fletcher Gross
Journal: Proc. Amer. Math. Soc. 31 (1972), 10-14
MathSciNet review: 0286856
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Abstract | References | Additional Information

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.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1972-0286856-7
PII: S 0002-9939(1972)0286856-7
Keywords: Finite automorphic algebra
Article copyright: © Copyright 1972 American Mathematical Society