Abstract:
This short article treats a very naive question concerning
roots of Möbius transformations in discrete groups. We exhibit,
according to the standard classification of Möbius
transformations, formulations depending on the types of given
transformations. Along the way, algebraic natures of relevant
subgroups of a discrete group under consideration are discussed,
which allows us to provide intuitive geometrical interpretations. We
indicate how the discreteness plays a substantial role during the
study while exploring folklore or classical results for these
subgroups. We conclude by remarking on the original motivation for
the study and point out possible directions for future research.
Key Words: Möbius transformations, roots, discrete
groups.
2010 Mathematics Subject Classification: Primary
22E40, 20H10; Secondary 30F35, 32G05.
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