HNN extension
Alright, kiddo, let's talk about HNN extensions!
Imagine you have a group of friends, but there's one friend who's a bit different from the rest. Let's call her Sally. Sally likes to do things her own way and sometimes it causes a bit of tension in the group.
In math, we have something like this called a subgroup. It's a smaller group within a bigger group that has its own rules and elements. Sally is like a subgroup within the bigger group of friends.
Now, let's say Sally wants to join another group of friends. But this new group has some rules that are different from the ones Sally is used to following. She still wants to be part of the group, but doesn't want to give up her old ways entirely.
In math, we call this situation an HNN extension. It's when we take a subgroup and add it to a bigger group, but we allow the elements in the subgroup to keep their own rules (they're called automorphisms).
So, basically, an HNN extension allows us to combine two groups that might have some differences and still keep some of the original group's character. It's like when Sally joins a new group, but is allowed to keep some of her quirks intact.
Imagine you have a group of friends, but there's one friend who's a bit different from the rest. Let's call her Sally. Sally likes to do things her own way and sometimes it causes a bit of tension in the group.
In math, we have something like this called a subgroup. It's a smaller group within a bigger group that has its own rules and elements. Sally is like a subgroup within the bigger group of friends.
Now, let's say Sally wants to join another group of friends. But this new group has some rules that are different from the ones Sally is used to following. She still wants to be part of the group, but doesn't want to give up her old ways entirely.
In math, we call this situation an HNN extension. It's when we take a subgroup and add it to a bigger group, but we allow the elements in the subgroup to keep their own rules (they're called automorphisms).
So, basically, an HNN extension allows us to combine two groups that might have some differences and still keep some of the original group's character. It's like when Sally joins a new group, but is allowed to keep some of her quirks intact.