Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On Klein's combination theorem. IV


Author: Bernard Maskit
Journal: Trans. Amer. Math. Soc. 336 (1993), 265-294
MSC: Primary 30F40
MathSciNet review: 1137258
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper contains an expansion of the combination theorems to cover the following problems. New rank $ 1$ parabolic subgroups are produced, while, as in previous versions, all elliptic and parabolic elements are tracked. A proof is given that the combined group is analytically finite if and only if the original groups are; in the analytically finite case, we also give a formula for the hyperbolic area of the combined group (i.e., the hyperbolic area of the set of discontinuity on the $ 2$-sphere modulo $ G$) in terms of the hyperbolic areas of the original groups. There is also a new variation on the first combination theorem in which the common subgroup has finite index in one of the two groups.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30F40

Retrieve articles in all journals with MSC: 30F40


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1137258-0
PII: S 0002-9947(1993)1137258-0
Article copyright: © Copyright 1993 American Mathematical Society