Abstract
Let S be a hyperbolic Riemann surface with a finite area. Let G be the covering group of S acting on the hyperbolic plane H. In this paper, the author studies some algebraic relations in the mapping class group of Ṡ for Ṡ = S\{a point}. The author shows that the only possible relations between products of two Dehn twists and products of mapping classes determined by two parabolic elements of G are the reduced lantern relations. As a consequence, a partial solution to a problem posed by J. D. McCarthy is obtained.
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