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The geometry of groups satisfying weak almost-convexity or weak geodesic-combability conditions

Tim R. Riley

Journal of Group Theory, 5(4), pages 513–525, 2002.

We examine the geometry of the word problem of two different types groups: those satisfying weak almost-convexity conditions and those admitting geodesic combings whose width satisfy minimally restrictive, non-vacuous constraints. In both cases we obtain an n! isoperimetric function and n2 bounds on the minimal isodiametric function and the filling length function.