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Original Articles

Bruck Loops with Abelian Inner Mapping Groups

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Pages 2449-2454 | Received 20 May 2010, Published online: 09 Jul 2012

REFERENCES

  • Aschbacher , M. , Kinyon , M. K. , Phillips , J. D. ( 2006 ). Finite Bruck loops . Transactions of the American Mathematical Society 358 : 3061 – 3075 .
  • Belousov , V. D. ( 1967 ). Foundations of the Theory of Quasigroups and Loops . Moscow : Izdat. Nauka, (Russian) .
  • Bruck , R. H. ( 1946 ). Contributions to the theory of loops . Trans. Amer. Math. Soc. 60 : 245 – 354 .
  • Bruck , R. H. ( 1971 ). A Survey of Binary Systems. Springer-Verlag .
  • Bruck R. H., Paige , L. J. ( 1956 ). Loops whose inner mappings are automorphisms . Ann. of Math. 63 ( 2 ): 308 – 323 .
  • Chein , O. ( 1978 ). Moufang loops of small order . Memoirs of the American Mathematical Society 13 ( 1 ): 197 .
  • Csörgo , P. ( 2007 ). Abelian inner mappings and nilpotency class greater than two . European J. Combin. 28 : 858 – 867 .
  • Csörgo , P. , Drápal , A. (2005). Left conjugacy closed loops of nilpotency class two. Results Math. 47:242–265.
  • Csörgo , P. , Kepka , T. ( 2004 ). On loops whose inner permutations commute . Comment. Math. Univ. Carolin. 45 : 213 – 221 .
  • Drápal , A. , Kinyon , M. K. Buchsteiner loops: associators and constructions. Submitted.
  • Drápal , A. , Vojtěchovský , P. ( 2008 ). Explicit constructions of loops with commuting inner mappings . European J. Combin. 29 : 1662 – 1681 .
  • Foguel , T. , Kinyon , M. K. , Phillips , J. D. ( 2006 ). On twisted subgroups and Bol loops of odd order . Rocky Mountain J. Math. 36 ( 1 ): 183 – 212 .
  • Glauberman , G. ( 1964 ). On loops of odd order I . J. Algebra 1 : 374 – 396 .
  • Glauberman , G. ( 1968 ). On loops of odd order II . J. Algebra 8 : 393 – 414 .
  • Hillenbrand , T. http://www.waldmeister.org
  • Kepka , T. ( 1998 ). On the abelian inner permutation groups of loops . Comm. Algebra 26 : 857 – 861 .
  • Kepka , T. , Phillips , J. D. ( 1997 ). Connected transversals to subnormal subgroups . Comment. Math. Univ. Carolin. 38 : 223 – 230 .
  • Kiechle , H. ( 2002 ). Theory of K-loops. Lecture Notes in Mathematics, 1778. Springer-Verlag .
  • Kinyon , M. K. , Phillips , J. D. , Robert , Veroff , Vojtěchovský , P. Moufang loops with abelian inner mapping groups. In preperation.
  • Kinyon , M. K. , Vojtěchovský , P. Autmorphic loops with abelian inner mapping groups. In preperation.
  • McCune , W. W. ( 2005 ). Prover9, automated reasoning software, and Mace4, finite model builder, Argonne National Laboratory. http://www.prover9.org
  • Nagy , G. P. , Vojtěchovský , P. ( 2009 ). Moufang loops with commuting inner mappings . Journal of Pure and Applied Algebra 213 ( 11 ): 2177 – 2186 .
  • Niemenmaa , M. ( 2009 ). Finite loops with nilpotent inner mapping groups are centrally nilpotent . Bull. Australian Math. Soc. 79 ( 1 ): 109 – 114 .
  • Niemenmaa , M. , Kepka , T. ( 1992 ). On connected transversals to abelian subgroups in finite groups . Bull. London Math. Soc. 24 : 343 – 346 .
  • Pflugfelder , H. O. ( 1990 ). Quasigroups and Loops: Introduction . Sigma Series in Pure Math. , 8. Berlin : Heldermann Verlag .
  • Phillips , J. D. , Stanovský , D. ( 2010 ). Automated theorem proving in quasigroup and loop theory . AI Communications 23 ( 2/3 ): 267 – 283 .
  • Communicated by I. Shestakov.

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