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(Link to SE duplicate: https://math.stackexchange.com/questions/4959071/are-group-theoretic-markov-properties-on-groups-with-decidable-word-problems) The Adian-Rabin theorem says that if a property of ...

Edited (this question contains two versions of a similar question) Is there some finitely presented group $G$ generated by $g_1,...,g_n$ such that there is an element $g\in G$ expressed as a finite ...

Let $r(m)$ denote the residue class $r+m\mathbb{Z}$, where $0 \leq r < m$. Given disjoint residue classes $r_1(m_1)$ and $r_2(m_2)$, let the class transposition $\tau_{r_1(m_1),r_2(m_2)}$ be the ...

Any finitely presented group naturally gives rise to an edge-labeled graph (the Cayley graph) and I am considering paths through this graph. Paths correspond to infinite sequences of generators, so ...