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Can you give me an example of a finitely generated infinitely presented amenable group which is a quotient of a finitely presented amenable group?

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    Lamplighter will not work because of a Theorem of R.Bieri and R.strebel which says: If $G$ is an infinitely presented metabelian group then any finitely presented covering group contains a nonabelian free group.2011-12-05

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An answer was given by Mark Sapir here:

https://mathoverflow.net/questions/82819/quotients-of-f-p-amenable-groups

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    You could accept your own answer so that this thread is considered as answered by the engine... :)2012-01-05