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Discreteness criteria for subgroups in SL(2, C)

Published online by Cambridge University Press:  01 July 1998

XIANTAO WANG  and
WEIQI YANG
XIANTAO WANG
Affiliation:
Department of Mathematics, Hunan University and Wuhan University, P.R. China
WEIQI YANG
Affiliation:
Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China
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Abstract

In this paper a new discreteness criterion for subgroups in SL(2, C) is established, which implies all known discreteness criteria by two-generator subgroup and is the best possible. And it is proved that every non-elementary and non-discrete subgroup of SL(2, C) has a non-elementary and non-discrete subgroup generated by two loxodromic elements.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 124 , Issue 1 , July 1998 , pp. 51 - 55
Copyright
Cambridge Philosophical Society 1998

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