Finite automorphic algebras over 𝐺𝐹(2)

Gross, Fletcher

doi:10.1090/S0002-9939-1972-0286856-7

Finite automorphic algebras over $\textrm {GF}(2)$
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by Fletcher Gross

Proc. Amer. Math. Soc. 31 (1972), 10-14

DOI: https://doi.org/10.1090/S0002-9939-1972-0286856-7

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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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Bibliographic Information

Journal: Proc. Amer. Math. Soc. 31 (1972), 10-14
DOI: https://doi.org/10.1090/S0002-9939-1972-0286856-7
MathSciNet review: 0286856