The Subgroups of the Generalized Finite Modular Group (Classic Reprint) - Hardcover

Eliakim Hastings Moore

 
9780266759898: The Subgroups of the Generalized Finite Modular Group (Classic Reprint)

Synopsis

A clear look at the structure of the generalized finite modular group and its subgroups.

This classic work shows what the groups are and how they behave, with key results and concrete examples.

The book introduces the modular group and its quotients, then classifies the subgroups into three broad kinds: metacyclic or solvable groups; groups with the abstract character of certain known groups; and other related structures. It presents important theorems about simplicity in specific cases and describes how conjugacy, generators, and cyclic subgroups fit together. The discussion also ties these ideas to related topics, including connections to automorphic functions and the broader landscape of finite and infinite group theory.
  • Learn how the generalized finite modular group is built from substitutions and matrices, and how its subgroups are organized.
  • See how simple, cyclic, and dihedral pieces arise within this framework, with explicit examples.
  • Understand how conjugacy and representations help classify the various subgroup types.
  • Explore the book’s links to automorphic functions and prior work in the field.
Ideal for readers with an interest in abstract algebra, group theory, and the interplay between finite groups and automorphic mathematics.

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