Weak Inverse Property Loops and Some Isotopy-Isomorphy Properties

Details Weak Inverse Property Loops and Some Isotopy-Isomorphy Properties Weak Inverse Property Loops and Some Isotopy-Isomorphy Properties

2007-06-11

arxiv.org/abs/0706.1481v1

Acta Universitatis Apulensis Mathematics-Informatics, Vol. 18 (2009), 19-33.

Mathematics

Group Theory

8 pages, submitted for publication

Scientific paper

Two distinct isotopy-isomorphy conditions, different from those of J. M. Osborn and Wilson's condition, for a weak inverse property loop(WIPL) are shown. Only one of them characterizes isotopy-isomorphy in WIPLs while the other is just a sufficient condition for isotopy-isomorphy. Under the sufficient condition called the ${\cal T}$ condition, Artzy's result that isotopic cross inverse property loops(CIPL) are isomorphic is proved for WIP loops.

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