The Class Equation for Finite Groups | Group Theory Tutorial!

We explain and derive the class equation for a finite group from the basics. We define what the conjugacy classes in a group are, and prove that they are equivalence classes for an equivalence relation (and thus partition the group into disjoint non-empty sets). We define the center of a group and explain the corresponding term in the class equation (the center consists precisely of the single element conjugacy classes). Finally, we define the centralizer of an element x in a group G and show that it is a subgroup, and its index (number of cosets) in G is equal to the size of the conjugacy class of x in G. The video is designed for students interested in group theory and especially more advanced concepts that lead to beautiful results and ideas in abstract algebra. If you enjoy this video, I would love if you could please like ✅ , subscribe 🎉, and share ⏩ with students, classmates, friends and family - it means so much to help support me in my goal of creating elite infinite free accessible math education worldwide! 😊 If you would like to support my channel beyond this (which of course would mean so much to me 🤗), please check out my "Patreon" page! The contributions here make a world of difference to helping me free up time to produce as much math content as possible (I currently do everything on my own), and there are also exclusive perks available when you signup (e.g., exclusive access to a private Discord server to chat and discuss math with me and other members, insider knowledge on my future YouTube content creation, priority replies to YouTube comments, public acknowledgements as a valued sponsor, a personalized thank you message etc.)! 😊 Become a Patreon Member 🤩:   / mathmasterywithamitesh   A HUGE thank you SO much to Alex and Stephan for their continued support of the channel as Ruby Members, and Nathan for their continued support of the channel as a Gold Member!! 🎊 My Channel Membership 🥇:    / @mathmasterywithamitesh   A HUGE thank you SO much to Aman, Julio, Stephan, Rob, Bernard, Louis and Harshavardhana for their continued support of the channel as Silver Members!! 🎉 You can also follow me on Instagram!   / math_mastery_with_amitesh