Talk:HNN extension

Group extension versus HNN extension
Just in case someone is curious: The HNN extension G* of G is not a group extension of G, because G is not normal in G*.

For instance, taking G to be the klein four group, and alpha to be the identity mapping on a subgroup of order 2, the resulting group is < a,b,t : aa = bb = abab = 1, bt=tb > with G being the subgroup . This has a quotient group < a,b,t : aa = bb = abab = 1, bt=tb, tt = (at)^4 = 1 > of order 16, and the image of  is not normal in the image of , so  is not normal in . JackSchmidt (talk) 19:57, 16 July 2008 (UTC)

Alternate form of Britton's lemma
This reformulation (inserted in 2008 by ) is wrong. Anne Bauval (talk) 14:39, 22 April 2024 (UTC)