Linear Groups with an Exposition, of the Galois Field Theory (Classic Reprint)

Explore the foundations of linear groups and their invariant forms.

This reference delves into the structure of linear groups with quadratic invariants and the role of orthogonal groups in understanding symmetry. The material highlights how different systems of simple groups relate through holoedric isomorphism and how these ideas fit into the broader landscape of group theory.

Readers will encounter a careful, step‑by‑step treatment of how substitutions preserve quadratic forms, how generators build orthogonal groups, and how these concepts connect to the known classifications of simple groups. The text blends theory with concrete results and historical context, helping you see the connections across chapters and topics.

• How quadratic invariants shape the structure and actions of linear groups
• Generators and relations that define orthogonal subgroups
• Connections between various group systems and their isomorphisms
• Historical development and key theorems in the classification of simple groups

Ideal for readers with a background in abstract algebra who want a rigorous, reference‑style overview of linear groups and their invariants.