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- W2114472114 abstract "If two loops are isomorphic, then it is shown that their holomorphs are also isomorphic. Conversely, it is shown that if their holomorphs are isomorphic, then the loops are isotopic. It is shown that a loop is a Smarandache loop if and only if its holomorph is a Smarandache loop. This statement is also shown to be true for some weak Smarandache loops(inverse property, weak inverse property) but false for others(conjugacy closed, Bol, central, extra, Burn, A-, homogeneous) except if their holomorphs are nuclear or central. A necessary and sufficient condition for theNuclear-holomorph of a Smarandache Bol loop to be a Smarandache Bruck loop is shown. Whence, it is found also to be a Smarandache Kikkawa loop if in addition the loop is a Smarandache A-loop with a centrum holomorph. Under this same necessary and sufficient condition, the Central-holomorph of a Smarandache A-loop is shown to be a Smarandache K-loop." @default.
- W2114472114 created "2016-06-24" @default.
- W2114472114 creator A5069204823 @default.
- W2114472114 date "2006-05-21" @default.
- W2114472114 modified "2023-09-27" @default.
- W2114472114 title "An holomorphic study of the Smarandache concept in loops" @default.
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- W2114472114 doi "https://doi.org/10.5281/zenodo.32297" @default.
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