Name: Inverse-Cycles in Weak-Inverse Loops
Creator: Artzy, Rafael
Keywords: Loops, quasigroups, 0101 mathematics, 16. Peace & justice, 01 natural sciences

Inverse-cycles in weak-inverse loops

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1978Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 68, page 132 (issn: 0002-9939,

Authors: Artzy, Rafael;

doi: 10.2307/2041755 , 10.1090/s0002-9939-1978-0463340-4

Inverse-Cycles in Weak-Inverse Loops

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Abstract

In a loop let J be the map taking every element into its right inverse. If the order of J is n, then { x , x J , … , x J n − 1 } \{ x,xJ, \ldots ,x{J^{n - 1}}\} is called an inverse-cycle of length n. If a weak-inverse loop consists only of the unit element and m inverse-cycles of length n, then n divides 2m.

Keywords

Loops, quasigroups

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