A Class of Loops Categorically Isomorphic to Bruck Loops of Odd Order

REFERENCES

• Aschbacher , M. ( 1998 ). Near subgroups of finite groups . J. Group Theory 1 : 113 – 129 .
   Web of Science ®Google Scholar
• Bruck , R. H. ( 1971 ). A Survey of Binary Systems . Berlin : Springer-Verlag .
   Google Scholar
• Burn , R. P. ( 1978 ). Finite Bol loops . Math. Proc. Cambridge Philos. Soc. 84 : 377 – 385 .
   Web of Science ®Google Scholar
• de Barros , D. A. S. , Grishkov , A. , Vojtěchovský , P. ( 2012 ). Commutative automorphic loops of order p 3 . Journal of Algebra and Its Applications 11 ( 05 ): 1250100 .
   Web of Science ®Google Scholar
• Foguel , T. , Kinyon , M. K. , Phillips , J. D. ( 2006 ). On twisted subgroups and Bol loops of odd order . Rocky Mountain J. Math. 36 : 183 – 212 .
   Web of Science ®Google Scholar
• Glauberman , G. ( 1964 ). On loops of odd order I . Journal of Algebra 1 : 374 – 396 .
   Google Scholar
• Glauberman , G. ( 1968 ). On loops of odd order II . Journal of Algebra 8 : 393 – 414 .
   Google Scholar
• The GAP Group ( 2008 ). Groups, Algorithms, and Programming, Available at http://www.gap-system.org (2008). Accessed January 2, 2013 .
   Google Scholar
• Isaacs , I. M. ( 2008 ). Finite Group Theory. Graduate Studies in Mathematics, AMS 92 .
   Google Scholar
• Jedlička , P. , Kinyon , M. K. , Vojtěchovský , P. ( 2010 ). Constructions of commutative automorphic loops . Comm. Algebra 38 : 3243 – 3267 .
   Web of Science ®Google Scholar
• Jedlička , P. , Kinyon , M. K. , Vojtěchovský , P. ( 2011 ). The structure of commutative automorphic loops . Trans. Amer. Math. Soc. 363 : 365 – 384 .
   Web of Science ®Google Scholar
• Jedlička , P. , Kinyon , M. K. , Vojtěchovský , P. ( 2012 ). Nilpotency in automorphic loops of prime power order . Journal of Algebra 350 : 64 – 76 .
   Web of Science ®Google Scholar
• Johnson , K. W. , Kinyon , M. K. , Nagy , G. P. , Vojtěchovský , P. ( 2011 ). Searching for small simple automorphic loops . LMS Journal of Computation and Mathematics 14 : 200 – 213 .
   Web of Science ®Google Scholar
• Kiechle , H. , Kinyon , M. K. ( 2004 ). Infinite simple Bol loops . Comment. Math. Univ. Carolin. 45 : 275 – 278 .
   Google Scholar
• Kinyon , M. K. , Vojtěchovský , P. ( 2009 ). Primary decompositions in varieties of commutative diassociative loops . Communications in Algebra 37 : 1428 – 1444 .
   Web of Science ®Google Scholar
• McCune , W. ( 2009 ). Prover9 and Mace4, http://www.cs.unm.edu/ᵯccune/prover9/. Accessed January 1, 2011 .
   Google Scholar
• Nagy , G. P. , Vojtěchovský , P. ( 2008 ). Loops: Computing with quasigroups and loops, http://www.math.du.edu/loops. Accessed January 11, 2013 .
   Google Scholar
• Pflugfelder , H. O. ( 1990 ). Quasigroups and Loops: Introduction. Sigma Series in Pure Math, Berlin .
   Google Scholar
• Robinson , D. A. ( 1966 ). Bol loops . Trans. Amer. Math. Soc. 123 : 341 – 354 .
   Google Scholar
• Robinson , D. A. ( 1972 ). Bol quasigroups . Publ. Math. Debrecen 19 : 151 – 153 .
   Google Scholar
• Communicated by I. Shestakov.
   Google Scholar