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IMI/Publicaţii/QRS/Ediţii/QRS v.11, n.1 (11), 2004/

Extensions of Latin subsquares and local embeddability of groups and group algebras

Authors: M. Ziman

Abstract

We will show that any “self-adjoint” Latin subsquare with constant diagonal can be extended to a Latin square with the same property. As a consequence, every loop with inverses satisfying the identity (xy)^(-1) = y^(-1)x^(-1) (an IAA loop for short) is locally embeddable into finite IAA loops, and its loop algebra is locally embeddable into loop algebras of finite IAA loops. The IAA property enables to extend this result to loop algebras with the natural involution arising from the inverse map on the loop. In particular, this is true for groups and their group algebras.

M. Ziman
Department of Algebra and Number Theory,
Faculty of Mathematics Physics and Informatics,
Comenius University,
Mlynská dolina,
842 48 Bratislava,
SLOVAKIA,
E-mail:



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