Subgroup membership in \(\mathrm{GL}(2, \mathrm{Z})\)

Analysis of algorithms and problem complexity (68Q25) General structure theorems for groups (20E34) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Computational methods for problems pertaining to group theory (20-08)

Cites Work

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The membership problem for 3-manifold groups is solvable
On the complexity of some extended word problems defined by cancellation rules
The Nielsen reduction and P-complete problems in free groups
Finite automata for Schreier graphs of virtually free groups
Topology of finite graphs
The occurrence problem for extensions of Abelian groups by nilpotent groups
Some algorithmic problems for solvable groups
Stallings foldings and subgroups of free groups
Coxeter groups, 2-completion, perimeter reduction and subgroup separability.
The complexity of compressed membership problems for finite automata
Stallings graphs for quasi-convex subgroups
Algorithmic problems for free-Abelian times free groups.
A FAST ALGORITHM FOR STALLINGS' FOLDING PROCESS
STALLINGS FOLDINGS AND SUBGROUPS OF AMALGAMS OF FINITE GROUPS
Subgroups of small Cancellation Groups
Decidability of the Membership Problem for 2 × 2 integer matrices
The Identity Problem for Matrix Semigroups in SL₂(ℤ) is NP-complete
FOLDINGS, GRAPHS OF GROUPS AND THE MEMBERSHIP PROBLEM
On homomorphisms onto finite groups
On the Identity Problem for the Special Linear Group and the Heisenberg Group.
Parallel complexity for nilpotent groups
Complexity and Randomness in Group Theory
Decidability of membership problems for flat rational subsets of GL(2, Q) and singular matrices
Membership Problem for the Modular Group
The Compressed Word Problem for Groups

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