Talk:HNN extension

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Field:  Algebra

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 <a,b>. 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 <a,b> is not normal in the image of <a,b,t>, so <a,b> is not normal in <a,b,t>. JackSchmidt (talk) 19:57, 16 July 2008 (UTC)