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Loops of Orderpn+1 with Transitive Automorphism Groups

✍ Scribed by Arthur A. Drisko

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 239 KB
Volume: 128
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.1997.1624

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✦ Synopsis

It is shown that isotopic loops of order p n +1, p a prime, which have transitive automorphism groups are in fact isomorphic. The proof uses the Sylow theorems to obtain an isomorphism from an arbitrary isotopism. The result is applied to the additive loops of neofields of order p n +1.

1997 Academic Press

An autotopism is an isotopism from a loop to itself. The set of autotopisms of a loop G forms a group A(G). An isomorphism is an isotopism for which :=;=#. Note that an isomorphism must take the identity of one loop to the identity of the other. The automorphism group, Aut(G), of a loop G article no. AI971624 36

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