The word problem in Hanoi Towers groups

• Published in: Algebra and Discrete Mathematics
• Date: 2014
• Main Author: Bondarenko, I.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2014
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/153336
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: The word problem in Hanoi Towers groups / I. Bondarenko // Algebra and Discrete Mathematics. — 2014. — Vol. 17, № 2. — С. 248–255. — Бібліогр.: 9 назв. — англ.

We prove that the elements of the Hanoi Towers groups Hm have depth bounded from above by a poly-logarithmic function O(logm⁻²n), where n is the length of an element. Therefore the word problem in groups Hm is solvable in subexponential time exp(O(logm⁻²n)).