A. Zastrow, CONSTRUCTION OF AN INFINITELY GENERATED GROUP THAT IS NOT A FREE PRODUCT OF SURFACE GROUPS AND ABELIAN-GROUPS, BUT WHICH ACTS FREELY ON AN R-TREE, Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 128, 1998, pp. 433-445
The existence of a group H as described in the title shows that the st
atement of Rips's Theorem for finitely generated groups cannot be exte
nded without further complications to infinitely generated groups. The
construction as given in this paper uses a careful combinatorial desc
ription of the fundamental group of the Hawaiian Earrings and a length
function that can be put on a special subgroup. Then the existence of
H follows using a theorem of Chiswell, Alperin and Moss.