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A conjecture on a class of elements of finite order in K2Fp

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Abstract

For a local field F the finite subgroups of K2 F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a conjecture posed by Browkin.

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References

  1. Tate, J., Relation between K2 and Galois cohomology, Invent. Math., 1976, 36: 257.

    Article  MATH  MathSciNet  Google Scholar 

  2. Suslin, A. A., Torsion in K2 of fields, K-Theory, 1987, 1: 5.

    Article  MathSciNet  Google Scholar 

  3. Moore, C., Group extensions of p-adic and adelic linear groups, Publ. Math. I. H. E. S., 1969, 35: 5.

    Google Scholar 

  4. Carroll, J. E., On the torsion in K2 of local fields, Lecture Notes in Math., Vol. 342, Berlin: Springer-Verlag, 1973, 464.

    Google Scholar 

  5. Tate, J., On the torsion in K2 of fields, Algebraic Number Theory, papers contributed for the International symposium, Kyoto 1976, 243.

  6. Merkujev, A. S., On the torsion in K2 of local fields, Annals of Mathematics, 1983, 118: 375.

    Article  MathSciNet  Google Scholar 

  7. Browkin, J., Elements of small order in K2 F, Algebraic K-Theory, Lecture Notes in Math., Vol. 966, Berlin-Heidelberg-New York: Springer-Verlag, 1982, 1–6.

    Google Scholar 

  8. Urbanowicz, J., On elements of given orders in K2 F, J. Pure. Appl. Alg., 1988, 50: 295.

    Article  MATH  MathSciNet  Google Scholar 

  9. Qin Hourong, Elements of finite order in K2F of fields, Chinese Science Bulletin, 1994, 38(24): 2227.

    Google Scholar 

  10. Qin Hourong, The 2-Sylow subgroups of K2OF for real quadratic fields F, Science in China (in Chinese), Ser. A, 1993, 23(12): 1254.

    Google Scholar 

  11. Qin Hourong, The 2-Sylow subgroups of the tame kernel of imagine quadratic fields, Acta Arith., 1995, 69: 153.

    MATH  MathSciNet  Google Scholar 

  12. Qin Hourong, The 4-rank of K2OF for real quadratic fields, Acta Arith., 1995, 72: 323.

    MATH  MathSciNet  Google Scholar 

  13. Qin Hourong, The subgroups of finite order in K2 ℚ. Algebraic K- Theory and Its Application ( eds. Bass, H., Kuku, A. O., Pedrini, C.), Singapore: World Scientific, 1999, 600–607.

    Google Scholar 

  14. Weiss, E., Algebraic Number Theory, New York: McGraw-Hill, 1963, 119–120, 185-186.

    MATH  Google Scholar 

  15. Iwasawa, K., Local Class Field Theory (in Chinese), Beijing: Science Press, 1986, 27–28, 129-130.

    Google Scholar 

  16. Neukirch, J., Class Field Theory, Berlin-Heidelberg: Springer-Verlag, 1986, 50.

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, 210093, Kanjing, China

    Kejian Xu

  2. Department of Mathematics, Qingdao University, 266071, Qingdao, China

    Kejian Xu & Hourong Qin

Authors
  1. Kejian Xu
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  2. Hourong Qin
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Xu, K., Qin, H. A conjecture on a class of elements of finite order in K2Fp . Sci. China Ser. A-Math. 44, 484–490 (2001). https://doi.org/10.1007/BF02881885

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  • DOI: https://doi.org/10.1007/BF02881885

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