Brauer–Nesbitt theorem
The Brauer-Nesbitt theorem is like a big puzzle about groups and the things that they are made of. It says that if you have a group and you want to look at all the different ways that you can break it up into smaller groups, you can use something called characters to help you. A character is like a special number that tells you something important about how the group behaves.
Now, if you have two characters that are the same, you can think of them as being like two puzzle pieces that fit together perfectly. And the Brauer-Nesbitt theorem says that if you have enough of these puzzle pieces that fit together, you can use them to figure out exactly how the group is put together.
So it's like you have a big box of puzzle pieces labeled with different numbers and you want to make a big picture by putting them together. The Brauer-Nesbitt theorem tells you which pieces to use and how to fit them together so you can see the whole picture.
Now, if you have two characters that are the same, you can think of them as being like two puzzle pieces that fit together perfectly. And the Brauer-Nesbitt theorem says that if you have enough of these puzzle pieces that fit together, you can use them to figure out exactly how the group is put together.
So it's like you have a big box of puzzle pieces labeled with different numbers and you want to make a big picture by putting them together. The Brauer-Nesbitt theorem tells you which pieces to use and how to fit them together so you can see the whole picture.