m at h . G M ] 1 1 Ju n 20 07 On A Pair Of Universal Weak Inverse Property Loops ∗ †
نویسنده
چکیده
A new condition called 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 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 T condition to be isomorphic is shown. A CIPL and an isomorph are observed to have this weak T condition.
منابع مشابه
ar X iv : 0 70 6 . 14 81 v 1 [ m at h . G R ] 1 1 Ju n 20 07 Weak Inverse Property Loops and Some Isotopy - Isomorphy Properties ∗ †
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 T condition, Artzy’s result that isotopic cross inverse property loops(CI...
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