The Conjugacy Problem in Free Solvable Groups and Wreath Products of Abelian Groups is in $${{\mathsf {T}}}{{\mathsf {C}}}^0$$

Alexei Miasnikov,Armin Weiß,Svetla Vassileva

doi:10.1007/978-3-319-58747-9_20

The Conjugacy Problem in Free Solvable Groups and Wreath Products of Abelian Groups is in $${{\mathsf {T}}}{{\mathsf {C}}}^0$$

Alexei Miasnikov, Armin Weiß + Show 1 more

https://doi.org/10.1007/978-3-319-58747-9_20

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Publication Date: Jan 1, 2017

Citations: 2

Affiliation: Stevens Institute of Technology, Champlain College

#Conjugacy Problem #Wreath Products Of Abelian Groups + Show 7 more

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Abstract

We show that the conjugacy problem in a wreath product $A \wr B$ is uniform-${{\mathsf {T}}}{{\mathsf {C}}}^0$-Turing-reducible to the conjugacy problem in the factors A and B and the power problem in B. Moreover, if B is torsion free, the power problem for B can be replaced by the slightly weaker cyclic submonoid membership problem for B, which itself turns out to be uniform-${{\mathsf {T}}}{{\mathsf {C}}}^0$-Turing-reducible to the conjugacy problem in $A \wr B$ if A is non-abelian.

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