On Groups whose Geodesic Growth is Polynomial
نویسندگان
چکیده
This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group G has an element whose normal closure is abelian and of finite index, then G has a finite generating set with respect to which the geodesic growth is polynomial (this includes all virtually cyclic groups).
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عنوان ژورنال:
- IJAC
دوره 22 شماره
صفحات -
تاریخ انتشار 2012