Coset construction
Imagine you have a bunch of toy cars, and you want to group them together based on their colors. You have a red car, a blue car, and a green car. You can make a group called "Red cars", which includes just the red car. You can also make a group called "Blue cars", which includes just the blue car. Finally, you can make a group called "Green cars", which includes just the green car.
But what if you want to make a group that includes all the cars that are not red? You can call this group the "Not Red cars". This group is made up of all the cars that are either blue or green. We can call this the "coset" of the group "Red cars". A coset is like a group that overlaps with another group, but doesn't contain all the same elements.
So in math, coset construction is when you take a group and a subgroup of that group, and you create a new group that includes all the elements in the subgroup, plus some extra elements from the original group that are not in the subgroup. This new group is called a coset of the subgroup. Just like with our toy cars, a coset is a way to group things together based on some criteria.
But what if you want to make a group that includes all the cars that are not red? You can call this group the "Not Red cars". This group is made up of all the cars that are either blue or green. We can call this the "coset" of the group "Red cars". A coset is like a group that overlaps with another group, but doesn't contain all the same elements.
So in math, coset construction is when you take a group and a subgroup of that group, and you create a new group that includes all the elements in the subgroup, plus some extra elements from the original group that are not in the subgroup. This new group is called a coset of the subgroup. Just like with our toy cars, a coset is a way to group things together based on some criteria.