An holomorphic study of Smarandache automorphic and cross inverse ploperty loops

Details An holomorphic study of Smarandache automorphic and cross inverse ploperty loops An holomorphic study of Smarandache automorphic and cross inverse ploperty loops

2008-02-11

arxiv.org/abs/0802.1415v3

Proceedings of the 4th International Conference on Number Theory and Smarandache Problems, Scientia Magna Journal. Vol. 4, No.

Mathematics

General Mathematics

9 pages

Scientific paper

By studying the holomorphic structure of automorphic inverse property quasigroups and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop if and only if its Smarandache automorphism group is trivial and the loop is itself is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop.

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