On a Pair of Universal Weak Inverse Property Loops

Details On a Pair of Universal Weak Inverse Property Loops On a Pair of Universal Weak Inverse Property Loops

2007-06-11

arxiv.org/abs/0706.1482v2

NUMTA Bulletin, Vol. 1(2009), 22-40.

Mathematics

General Mathematics

14 pages.

Scientific paper

A new condition called ${\cal T}$ condition is introduced for the first time and used to study a pair of isotopic loops. Under this condition, a loop in the pair is a WIPL if and only if the other loop is a WIPL. Furthermore, such WIPLs are isomorphic. The translation elements $f$ and $g$ of a CIPL with the ${\cal T}$ condition(such that its $f,g$-isotope is an automorphic inverse property loop) are found to be alternative, flexible, centrum and equal elements. A necessary and sufficient condition for a pair WIPLs with a weak ${\cal T}$ condition to be isomorphic is shown. A CIPL and an isomorph are observed to have this weak ${\cal T}$ condition.

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