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Multiplication Groups of Loops and Projective Semilinear Transformations in Dimension Two

✍ Scribed by Aleš Drápal

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 187 KB
Volume: 251
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9120

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✦ Synopsis

For a loop Q denote by Mlt Q the permutation group generated by translations

where F is a finite field with at least five elements, and if Mlt Q ≤ PΓL 2 F , then Q is an abelian group. The same result holds for an infinite field F, if the automorphisms associated with translations generate a finite subgroup of Aut F .  2002 Elsevier Science (USA)

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