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Algebras with Transitive Automorphism Groups

Published online by Cambridge University Press:  20 November 2018

L. G. Sweet  and
J. A. MacDougall
L. G. Sweet
Affiliation:
Department of Mathematics & Computer Science, University of Prince Edward Island, Charlottetown, Prince Edward IslandCIA 4P3
J. A. MacDougall
Affiliation:
Department of Mathematics & Computer Science, University of Prince Edward Island, Charlottetown, Prince Edward IslandCIA 4P3
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Abstract

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Let A be a finite dimensional algebra (not necessarily associative) over a field, whose automorphism group acts transitively. It is shown that K = GF(2) and A is a Kostrikin algebra. The automorphism group is determined to be a semi-direct product of two cyclic groups. The number of such algebras is also calculated.

Keywords

primary 17A99secondary 20B25Transitive groupsautomorphism groupsKostrikin algebrashomogeneous algebrasautomorphic algebras
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 2 , 01 June 1986 , pp. 224 - 226
Copyright
Copyright © Canadian Mathematical Society 1986

References

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