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G-Loops and Permutation Groups

✍ Scribed by Kenneth Kunen

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
131 KB
Volume
220
Category
Article
ISSN
0021-8693

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✦ Synopsis

A G-loop is a loop which is isomorphic to all its loop isotopes. We apply some theorems about permutation groups to get information about G-loops. In particular, we study G-loops of order pq, where p < q are primes and p q -1 . In the case p = 3, the only G-loop of order 3q is the group of order 3q. The notion "G-loop" splits naturally into "left G-loop" plus "right G-loop." There exist non-group right G-loops and left G-loops of order n iff n is composite and n > 5.

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