[PDF][PDF] AN HOLOMORPHIC STUDY OF THE SMARANDACHE CONCEPT IN LOOPS

SCIN LOOPS - arXiv preprint math/0701853 - researchgate.net
SCIN LOOPS
arXiv preprint math/0701853researchgate.net
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 …
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 the Nuclear-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.
researchgate.net
以上显示的是最相近的搜索结果。 查看全部搜索结果