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Open Access Publications from the University of California

On quasihomomorphisms with noncommutative targets

  • Author(s): Fujiwara, K
  • Kapovich, M
  • et al.

© 2016, Springer International Publishing. We describe structure of quasihomomorphisms from arbitrary groups to discrete groups. We show that all quasihomomorphisms are “constructible”, i.e., are obtained via certain natural operations from homomorphisms to some groups and quasihomomorphisms to abelian groups. We illustrate this theorem by describing quasihomomorphisms to certain classes of groups. For instance, every unbounded quasihomomorphism to a torsion-free hyperbolic group H is either a homomorphism to a subgroup of H or is a quasihomomorphism to an infinite cyclic subgroup of H.

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