INVESTIGATING ALGEBRAIC SIMPLE GROUPS WITH CONJUGACY CLASSES AND PRODUCTS.

Algebraic simple groups, being non-abelian and lacking proper normal subgroups, represent a profound and captivating domain within group theory and algebraic geometry. In the pursuit of understanding these enigmatic entities, the study of conjugacy classes and products emerges as a key to unlocking their underlying symmetries and structures. Group members can be partitioned into different sets with the use of conjugacy classes, which group together equivalent elements under inner automorphisms to show similar algebraic features. The analysis of conjugacy classes provides deep insights into the dynamics and character of algebraic simple groups. On the other hand, group products explore the interactions between distinct elements, generating new elements within the group and unraveling its internal symmetries. [ABSTRACT FROM AUTHOR]