A geometric approach to the almost convexity and growth of some nilpotent groups

DOI10.1007/BF01452050zbMath0693.20037MaRDI QIDQ584409

Michael Shapiro

Publication date: 1989

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164620

zbMATH Keywords

Cayley graphgeneratorsdiscrete Heisenberg groupalmost convexitycone typesgrowth-series

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Nilpotent groups (20F18) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items

The Hilbert series of prime PI rings., Almost convex groups and the eight geometries, The rationality of Sol-manifolds, Infinite geodesics in the discrete Heisenberg group, Growth of a PSL₂R Manifold Group, On problems related to growth, entropy, and spectrum in group theory, The Heisenberg group is pan-rational, Asymptotics of the number of geodesics in the discrete Heisenberg group, Growth series for the group \(\langle x,y\mid x^{-1}yx=y^ l\rangle\), Rational Growth and Almost Convexity of Higher-Dimensional Torus Bundles

Cites Work

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• The combinatorial structure of cocompact discrete hyperbolic groups
• Almost convex groups
• Solvgroups are not almost convex
• The Geometries of 3-Manifolds