known as combinatorial group theory, the word problem for a finitely generated group G {\displaystyle G} is the algorithmic problem of deciding whether two...

situations Word problem (mathematics), a decision problem for algebraic identities in mathematics and computer science Word problem for groups, the problem of...

as a reduced word in S. Word problem (mathematics) Word problem for groups for example, fdr1 and r1fc in the group of square symmetries for example, xy...

to a set of rewriting identities. A prototypical example is the word problem for groups, but there are many other instances as well. Some deep results...

{\displaystyle \leq 1} is undecidable. The word problem for groups. The conjugacy problem. The group isomorphism problem. Determining whether two finite simplicial...

finitely presented groups. By the word problem for groups, which is equivalent to the halting problem, it is impossible to classify such groups, so a full topological...

the word problem for groups; and the classical Burnside problem. See the book by Chandler and Magnus for a detailed history of combinatorial group theory...

relations. The negative solution to the word problem for groups states that there is a finite presentation ⟨S | R⟩ for which there is no algorithm which, given...

schools. One of the first problems suspected to be undecidable, in the second sense of the term, was the word problem for groups, first posed by Max Dehn...

unlike the Todd–Coxeter algorithm, it can sometimes solve the word problem for infinite groups. The main practical difficulties in producing a coset enumerator...

diffeomorphism or homeomorphism in dimensions ≥ 4 – because the word problem for groups cannot be solved – but it is possible to classify manifolds up...

are impossible to classify, as this is harder than solving the word problem for groups. Simply connected compact 5-manifolds were first classified by...

Muller–Schupp theorem states that a finitely generated group G has context-free word problem if and only if G is virtually free. The theorem was proved...

from Yorkshire who worked in combinatorial group theory and was an expert on the word problem for groups. Britton was a member of the London Mathematical...

Novikov is known for his work on combinatorial problems in group theory: the word problem for groups, and his progress in the Burnside problem. In 1955, he...

lemma Partial word Shift space Word metric Word problem (computability) Word problem (mathematics) Word problem for groups Young–Fibonacci lattice Berstel...

interstellar and circumstellar molecules Smallest grammar problem Word problem for groups Marshall SM, Mathis C, Carrick E, et al. (24 May 2021). "Identifying...

it homeomorphic to a manifold? The problem is undecidable; the proof is by reduction from the word problem for groups.: 11  Stillwell, John (1993), Classical...

just a group with exponent n. The Burnside problem for groups with bounded exponent asks: Burnside problem I. If G is a finitely generated group with exponent...

Entscheidungsproblem Halting problem Correctness Post correspondence problem Decidable language Undecidable language Word problem for groups Wang tile Penrose tiling...

groups for which the restriction of the isomorphism problem is known to be decidable. They include finitely generated abelian groups, finite groups,...

science. Group theory is also central to public key cryptography. Central extension Direct product of groups Direct sum of groups Extension problem Free abelian...

rationals Plastic ratio – Number, approximately 1.3247 Word problem for groups – Problem in finite group theory O'Connor, John J.; Robertson, Edmund F., "Axel...

Year 2000 problem, it made Microsoft Word 5.5 for DOS available for free downloads. As of February 2021[update], it is still available for download from...

(1957, mathematics, for proving the undecidability of the word problem for groups) Sergei Prokofiev (1957, music, posthumously, for his Symphony No. 7)...

word problem for groups was proved algorithmically unsolvable by Pyotr Novikov in 1955 and independently by W. Boone in 1959. The busy beaver problem...

Pyotr Sergeyevich Novikov, who gave a negative solution to the word problem for groups. His mother, Lyudmila Vsevolodovna Keldysh, and maternal uncle...

of a group Word problem for groups Quotient group Extension problem Direct sum, direct product Semidirect product Wreath product Types Simple group Finite...

nigger have been increasingly replaced by the euphemistic contraction "the N-word", notably in cases where nigger is mentioned but not directly used. In an...

that the word problem for groups is not effectively solvable: there is no effective procedure that, given a word in a finitely presented group, will decide...