168
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Topological Right Gyrogroups and Gyrotransversals

&
Pages 3559-3575 | Received 29 Oct 2011, Published online: 21 Jun 2013

REFERENCES

  • Adams , J. F. ( 1960 ). On the non-existence of Hopf invariant one . Ann. Math. 72 : 20 – 104 .
  • Albert , A. A. ( 1943 ). Quasigroups I . Trans. Amer. Math. Soc. 54 : 507 – 519 .
  • Albert , A. A. ( 1944 ). Quasigroups II . Trans. Amer. Math. Soc. 55 : 401 – 419 .
  • Arens , R. ( 1946 ). Topology for homeomorphism groups . Am. J. Math. 68 : 593 – 610 .
  • Baer , R. ( 1939 ). Nets and groups . Trans. Amer. Math. Soc. 46 : 110 – 141 .
  • Brill , A. V. ( 1972 ). Das Relativitatsprinzip . Deutsch. Math.-Verein. 21 : 60 – 87 .
  • Bruck , R. H. ( 1946 ). Contributions to the theory of Loops . Trans. Amer. Math. Soc. 60 : 245 – 354 .
  • Dieck , T. T. ( 1987 ). Transformation Groups . Berlin : Walter De-grueter .
  • Dugundji , J. ( 1975 ). Topology . New Delhi : Prentice Hall of India .
  • Feder , T. ( 2003 ). Strong near subgroups and left gyrogroups . Journal of Algebra 259 : 177 – 190 .
  • Feldman , J. , Greeleaf , F. P. ( 1968 ). Existence of Borel transversals in groups . Pac. J. Maths 25 ( 3 ): 455 – 461 .
  • Foguel , T. , Ungar , A. A. ( 2000 ). Involutory decomposition of groups into twisted subgroups and subgroups . J. Group Theory 3 : 27 – 46 .
  • Foguel , T. , Ungar , A. A. ( 2001 ). Gyrogroups and the decomposition of groups into twisted subgroups and subgroups . Pac. J. Maths. 197 ( 1 ).
  • Hewitt , E. , Ross , K. A. ( 1963 ). Abstract harmonic analysis I . Berlin : Springer-Verlag .
  • Kiechle , H. ( 2002 ). Theory of K-loops. Lecture Notes, A.M.S. 1778 .
  • Kuznetsov , E. ( 2003 ). Gyrogroups and left gyrogroups as transversals of special kind . Alg. and Discrete Maths. 3 : 58 – 81 .
  • Lal , R. ( 1996 ). Transversals in groups . Journal of Algebra 181 : 70 – 81 .
  • Lal , R. , Sharma , B. K. ( 2010 ). Pseudocohomology of general extensions . Homology, Homotopy and Applications 12 ( 2 ): 147 – 165 .
  • Lal , R. , Shukla , R. P. ( 2005 ). Transversals in Non-discrete groups . Proc. Indian Acad. Sci. (Math. Sci.) 115 ( 4 ): 429 – 435 .
  • Lal , R. , Yadav , A. C. ( 2010 ). Smooth right quasigroup structures on 1-manifolds . J. Math. Sci. Univ. Tokyo 17 : 313 – 321 .
  • Lal , R. , Yadav , A. C. ( 2011 ). Twisted Right Gyrogroups and Twisted Gyrotransversals. Preprint 2011 .
  • Lang , S. ( 2006 ). Algebra, Rev. 3rd ed. Springer (GTM 211), Second Indian reprint .
  • Yu. Ol'shanskii , A. ( 1991 ). Geometry of Defining Relations in Groups. Netherlands, (English ed.) Kluwer Academy Pub .
  • Shelah , S. ( 1980 ). On a Problem of Kurosh, Jo'nsson Group and Applications. Word Problems, II (Conf. on Decision Problems in Algebra, Oxford, 1976), Stud. Logic Foundations Math. Vol. 95, Amsterdam-New York: North-Holland, pp. 373–394 .
  • Ungar , A. A. ( 1997 ). Thomas precession: its underlying gyrogroup axioms and their use in hyperbolic geometry and relativity physics . Found. Physics 27 : 881 – 951 .
  • Communicated by A. Olshanskii.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.