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Home  >  Volume 22 (2012)

Nuclear Automorphism of a class of Osborn Loops by John Olusola Adeniran and 2*Abednego Orobosa Isere, Volume 22 (November, 2012), pp 5 – 8
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Let (L,∙) be any loop and ∅ an automorphism of L into L such that x∅y∙zx=x∅(yz∙x) 

∀ x,y,z ∈L.Then, it is shown that  A(L) -holomorph (H,∘) of (L,∙) is an Osborn loop with inverse property where A(L) is a group of all automorphisms of (L,∙). Moreover, it is established that (H,∘) is an Osborn loop whenever x^λ∙x∅ is in the nucleus of (L,∙) and thus making each of the automorphisms of (L,∙)  a nuclear automorphism.

2000 Mathematics Subject Classification. Primary 20N05; Secondary 08A05 

Keywords :Osborn loops, isotopism, autotopism, Nuclear Automorphism.