On the lattice formed by all normal subloops of a finite loop |
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Authors: | Huberta Lausch |
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Institution: | (1) Mathematisches Institut, Universität Würzburg, Am Hubland, D-97074 Würzburg, Germany |
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Abstract: | All normal subloops of a loopG form a modular latticeL
n
(G). It is shown that a finite loopG has a complemented normal subloop lattice if and only ifG is a direct product of simple subloops. In particular,L
n
(G) is a Boolean algebra if and only if no two isomorphic factors occurring in a decomposition ofG are abelian groups. The normal subloop lattice of a finite loop is a projective geometry if and only ifG is an elementary abelianp-group for some primep. |
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Keywords: | 20N05 06C99 51E99 |
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