本論文主要研究麥凱猜想（McKay Conjecture）在對稱群與交錯群上的成立情形。第一章介紹群表示論的基本概念與相關理論，作為後續研究之基礎。第二章說明麥凱猜想的內容，並介紹一些與其相關的重要猜想。第三章證明麥凱猜想對於對稱群成立；第四章則進一步證明麥凱猜想對於交錯群亦成立。最後，在第五章中，利用 GAP 電腦代數系統驗證 Isaacs–Navarro 猜想的相關結果。

This thesis studies the validity of the McKay Conjecture for symmetric groups and alternating groups. Chapter 1 provides the necessary background on the representation theory of finite groups, which serves as the foundation for the subsequent chapters. Chapter 2 introduces the McKay Conjecture and discusses several related conjectures. Chapter 3 proves the McKay Conjecture for symmetric groups, while Chapter 4 establishes the conjecture for alternating groups. Finally, Chapter 5 uses the GAP computer algebra system to verify the Isaacs--Navarro Conjecture.

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