EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 41(55), pp. 49--52 (1987)

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ON AUTOMORPHISM GROUPS OF NON-ASSOCIATIVE BOOLEAN RINGS

Sin-Min Lee

Dept. of Maths. and Computer Science San Jose State University, San Jose, California 95192, USA

Abstract: The present paper is concerned with the study of $\Aut(B(n))$ the automorphism group of a non-associative Boolean rings $B(n)$, where $\left$ is a free 2-group on n generators $\{x_i\}$ $i=1,\dots,n$, subject with $X_i\circ X_j=X_i+X_j$ for $i\neq j$. It is shown that for $n$ even, Aut$(B(n))=S_{n+1}$ and for $n$ odd, Aut$(B(n))=S_n$. An example of a non-associative Boolean ring $R$ of order 8 is provided which shows that in general Aut$(R)$ is not a symmetric group.

Classification (MSC2000): 17A36

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Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
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