Finite subgroups of the extended modular group
Gregory Dresden, Prakriti Panthi, Anukriti Shrestha, Jiahao Zhang
TL;DR
This paper classifies all finite subgroups of the extended modular group PGL(2,Z), identifying exactly seven conjugacy classes with specific sizes, thus providing a complete structural understanding.
Contribution
It provides a complete classification of finite subgroups of PGL(2,Z), detailing their sizes and conjugacy classes, which was previously unknown.
Findings
Exactly seven finite subgroups up to conjugacy
Subgroups of sizes 1, 2, 3, 4, and 6 identified
No other finite subgroups exist in PGL(2,Z)
Abstract
We show that in the extended modular group PGL(2,Z) there are exactly seven finite subgroups up to conjugacy; three subgroups of size 2, one subgroup each of size 3, 4, and 6, and the trivial subgroup of size 1.
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Taxonomy
TopicsFinite Group Theory Research · Geometric and Algebraic Topology · Advanced Topology and Set Theory