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Hydra group doubles are not residually finite

Hydra group doubles are not residually finite Abstract In 2013, Kharlampovich, Myasnikov, and Sapir constructed the first examples of finitely presented residually finite groups with large Dehn functions. Given any recursive function f , they produce a finitely presented residually finite group with Dehn function dominating f . There are no known elementary examples of finitely presented residually finite groups with super-exponential Dehn function. Dison and Riley’s hydra groups can be used to construct a sequence of groups for which the Dehn function of the k th group is equivalent to the k th Ackermann function. Kharlampovich, Myasnikov, and Sapir asked whether or not these groups are residually finite. We show that these constructions do not produce residually finite groups. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

Hydra group doubles are not residually finite

Pueschel, Kristen
Groups Complexity Cryptology , Volume 8 (2) – Nov 1, 2016
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Publisher
de Gruyter
Copyright
Copyright © 2016 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2016-0015
Publisher site
See Article on Publisher Site

Abstract

Abstract In 2013, Kharlampovich, Myasnikov, and Sapir constructed the first examples of finitely presented residually finite groups with large Dehn functions. Given any recursive function f , they produce a finitely presented residually finite group with Dehn function dominating f . There are no known elementary examples of finitely presented residually finite groups with super-exponential Dehn function. Dison and Riley’s hydra groups can be used to construct a sequence of groups for which the Dehn function of the k th group is equivalent to the k th Ackermann function. Kharlampovich, Myasnikov, and Sapir asked whether or not these groups are residually finite. We show that these constructions do not produce residually finite groups.

Journal

Groups Complexity Cryptology – de Gruyter

Published: Nov 1, 2016

References

  • The engulfing property for 3-manifolds
  • The optimal isoperimetric inequality for torus bundles over the circle
  • Subgroup separability, knot groups and graph manifolds
  • Residual properties of free products
  • Hydra groups
  • The optimal isoperimetric inequality for torus bundles over the circle
  • Residual properties of free products
  • Doubles of residually solvable groups
  • Residually finite HNN extensions
  • Doubles of residually solvable groups
  • A note on groups with separable finitely generated subgroups
  • Residually finite HNN extensions
  • A note on groups with separable finitely generated subgroups
  • The engulfing property for 3-manifolds
  • Hydra groups
  • Subgroup separability, knot groups and graph manifolds