P-compact group
A p-compact group is like a group made up of different pieces that all fit together really well. Each piece is called a "p-subgroup" and they all work together to make up the larger group. It's like building a big toy spaceship with a bunch of smaller blocks that fit perfectly together.
But there's a special rule for these p-subgroups, which is why they're called "p-compact." Each subgroup has to have a certain property that makes them "compact" when it comes to the number of elements in them. This makes the whole group act in a certain way that's really useful for solving certain math problems.
It's kind of like having a puzzle with lots of different pieces, but they all fit together in a specific way that makes it easy to solve. A p-compact group is just like that, but instead of a puzzle, it's a group of mathematical objects that work together in a specific way.
But there's a special rule for these p-subgroups, which is why they're called "p-compact." Each subgroup has to have a certain property that makes them "compact" when it comes to the number of elements in them. This makes the whole group act in a certain way that's really useful for solving certain math problems.
It's kind of like having a puzzle with lots of different pieces, but they all fit together in a specific way that makes it easy to solve. A p-compact group is just like that, but instead of a puzzle, it's a group of mathematical objects that work together in a specific way.