I have a question.

Let be a HNN extension of base group with stable letter .

Is it true that ?

I think is it true.

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- February 23rd 2010, 03:16 AMdeniselim17HNN extension
I have a question.

Let be a HNN extension of base group with stable letter .

Is it true that ?

I think is it true. - February 23rd 2010, 03:57 AMtonio

As an HNN extension , we have that in fact , for some isomorphism .

Since you give , this means you chose = the inverse involution automorphism of , so your group is the amalgamated product (as any other HNN extension) of with itself via the above involution.

As t is a "foreign" letter to the group then clearly

Tonio - February 23rd 2010, 06:46 AMSwlabr
HNN-extensions were constructed to show that we can embed a group in another group in a special way (if we are given two isomorphic subgroups of a group then the group can be embedded in a bigger group such that these groups are conjugate. I can't remember who asked this question - anyone know? It's been bugging me since I started typing this!) So, without proving anything you know that if then and clearly .

My point is that the result is clear and is the whole point of HNN-extensions! Although it does still require proof...