A Formalization of Finite Group Theory

Finite Group Theory

In the preface of Finite Group Theory the author, I. Martin Isaacs, states that his principal reason for writing the book was to expose students to the beauty of the subject. Finite group theory is indeed a subject which has both beautiful theory and beautiful examples. The simplicity and elegance of the group axioms have made group theory an almost universal choice as a starting point in the t...

A Modular Formalisation of Finite Group Theory

In this paper, we present a formalisation of elementary group theory done in Coq. This work is the first milestone of a long-term effort to formalise Feit-Thompson theorem. As our further developments will heavily rely on this initial base, we took special care to articulate it in the most compositional way. Key-words: finite groups, proof assistants, formalisation of mathematics ∗ Microsoft Re...

A Course in Finite Group Representation Theory

Notes on finite group theory

2 Preface Group theory is a central part of modern mathematics. Its origins lie in geometry (where groups describe in a very detailed way the symmetries of geometric objects) and in the theory of polynomial equations (developed by Galois, who showed how to associate a finite group with any polynomial equation in such a way that the structure of the group encodes information about the process of...

A Group Theoretical Formalization of Contact Motion

The work reported in this paper applies group theory to characterize local surface contact among solids, and makes such a formalization computationally tractable. This paper serves three purposes: (1) to report a new treatment of contacting surfaces as oriented sets and to verify the consistency of their corresponding symmetry groups in a group theoretical formalization framework; (2) to give a...