Dear friends, Since noone has yet answered this question, I volunteer. If one
kills the generators of the "base group", the quotient is isomorphic to the
infinite cyclic group with presentation <t| >. So the stable letter t maps
to a generator of Z, and thus has infinite order in the HNN group.
(Geometrically, the "torus" collapses onto the "core S^1".)
Best regards, Michael Falk.
>
> Dear Gap-Forum,
>
> I have a conceptual question concerning "HNN extensions".
>
> In the book
>
> B. Chandler / W. Magnus, "The History of Combinatorial Group Theory" (1982)
>
> on page 111, the definition of the HNN extension is given. It is followed
> by the remark: "In particular, t (the "stable letter") is always of infinite
> order in H (the extended group)."
>
> Is this remark really correct - and if, then why ?
>
> Thank you!
> --Toni
>
>