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Equations in Self-Similar Groups

Bag om Equations in Self-Similar Groups

We develop a toolkit to decide some quadratic equations with constants in certain self-similar groups and determine conditions under which these tools work. It turns out that for explicitly given groups the question of solvability of some equations reduces to a large but finite number of calculations. For special cases we provide the algorithms in the GAP language and use the computed results to verify that for example the Gupta-Sidki has commutator width at most 3.

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  • Sprog:
  • Engelsk
  • ISBN:
  • 9786202322713
  • Indbinding:
  • Paperback
  • Sideantal:
  • 148
  • Udgivet:
  • 9. august 2018
  • Størrelse:
  • 229x152x9 mm.
  • Vægt:
  • 227 g.
  • 2-3 uger.
  • 2. december 2024

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We develop a toolkit to decide some quadratic equations with constants in certain self-similar groups and determine conditions under which these tools work. It turns out that for explicitly given groups the question of solvability of some equations reduces to a large but finite number of calculations. For special cases we provide the algorithms in the GAP language and use the computed results to verify that for example the Gupta-Sidki has commutator width at most 3.

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