Multiply transitive group
Okay, imagine you have a bunch of toys that you want to arrange in different ways. Let's say you have three toys: a ball, a car, and a teddy bear.
Now, you want to move these toys around and put them in different spots. But some moves are more important than others. For example, switching the ball and the car is a big change, while just moving the ball a little closer to the teddy bear isn't a big deal.
When you start making lots of moves and changing the position of the toys, you might notice something interesting. Some moves let you switch any two toys you want, and other moves let you switch any three toys you want. You might even find some moves that let you switch any four toys you want!
In math, we call this kind of thing a "multiply transitive group". "Multiply transitive" means that you can switch lots of different things around, and "group" just means that all the moves you can make together form a special kind of pattern.
So, a multiply transitive group is a special kind of pattern that tells you how you can move things around. Just like with your toys, some moves let you switch just one thing, while others let you switch a whole bunch of things. And by studying these patterns, mathematicians can learn all sorts of cool things about how things move and change in different ways.
Now, you want to move these toys around and put them in different spots. But some moves are more important than others. For example, switching the ball and the car is a big change, while just moving the ball a little closer to the teddy bear isn't a big deal.
When you start making lots of moves and changing the position of the toys, you might notice something interesting. Some moves let you switch any two toys you want, and other moves let you switch any three toys you want. You might even find some moves that let you switch any four toys you want!
In math, we call this kind of thing a "multiply transitive group". "Multiply transitive" means that you can switch lots of different things around, and "group" just means that all the moves you can make together form a special kind of pattern.
So, a multiply transitive group is a special kind of pattern that tells you how you can move things around. Just like with your toys, some moves let you switch just one thing, while others let you switch a whole bunch of things. And by studying these patterns, mathematicians can learn all sorts of cool things about how things move and change in different ways.