Group extension

A group extension is like a puzzle that joins two smaller puzzles to make a bigger puzzle.

Imagine you have two puzzles: one with three pieces and the other with two pieces. If you join them together in a specific way, you can make a bigger puzzle with five pieces.

In math, this is similar to a group extension. A group is like a puzzle, but instead of pieces, it has elements. A group can be made up of smaller groups or subgroups, just like a puzzle can be made up of smaller puzzles.

If you have two groups, for example Group A and Group B, you can create a bigger group by joining them together in a certain way. This bigger group is called a group extension.

To make a group extension, there are certain rules that need to be followed. One important rule is that the new group needs to contain both Group A and Group B as subgroups. Another rule is that the elements of Group A and Group B need to interact in a specific way to form the new group.

This might seem complicated at first, but it's like putting together a puzzle: once you understand the rules and how the pieces fit together, it becomes easier to see the bigger picture.