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The discrete subgroups and Jørgensen’s inequality for SL(m,ℂ p )

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Abstract

In this paper, we give discreteness criteria of subgroups of the special linear group on ℚ p or ℂ p in two and higher dimensions. Jørgensen’s inequality gives a necessary condition for a non-elementary group of Möbius transformations to be discrete. We give a version of Jørgensen’s inequality for SL(m,ℂ p ).

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Authors and Affiliations

  1. Department of Mathematics, Fudan University, Shanghai, 200433, P. R. China

    Wei Yuan Qiu

  2. Institute of Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, P. R. China

    Jing Hua Yang

  3. Department of Mathematics, Zhejiang University, Zhejiang, 310027, P. R. China

    Yong Cheng Yin

Authors
  1. Wei Yuan Qiu
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  2. Jing Hua Yang
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  3. Yong Cheng Yin
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Corresponding author

Correspondence to Wei Yuan Qiu.

Additional information

Supported by National Natural Science Foundation of China (Grants Nos. 10831004 and 11271047) and by Science and Technology Commission of Shanghai Municipality NSF (Grant No. 10ZR1403700)

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Qiu, W.Y., Yang, J.H. & Yin, Y.C. The discrete subgroups and Jørgensen’s inequality for SL(m,ℂ p ). Acta. Math. Sin.-English Ser. 29, 417–428 (2013). https://doi.org/10.1007/s10114-013-1606-5

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  • DOI: https://doi.org/10.1007/s10114-013-1606-5

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