AUTOMATIC GROUPS, RATIONAL GROWTH, AND POLYGONAL AMALGAMS

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ACKNOWLEDGMENT

Work supported by NSF-REU grant DMS-9424098 and NSF-RUI grant DMS-9705007. We thank the referee for comments that improved the presentation of this paper.

Notes

^*That is, if two edges intersect in a vertex, then the intersection of the corresponding edge groups in the vertex group is the image of the center group in the vertex group.

^*A polygon of groups is proper if the center group is a proper subgroup of every edge group, and the edge groups are proper subgroups of the corresponding vertex groups.

^*The embedding of W into X is length preserving if the minimal length expression of any element w ∈ W in terms of the generators of W is the same as the minimal length expression of w in the generators of X.