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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On Klein’s combination theorem. IV
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by Bernard Maskit PDF
Trans. Amer. Math. Soc. 336 (1993), 265-294 Request permission

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.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 336 (1993), 265-294
  • MSC: Primary 30F40
  • DOI: https://doi.org/10.1090/S0002-9947-1993-1137258-0
  • MathSciNet review: 1137258