Fast Searching for Andrews-Curtis Trivializations
نویسندگان
چکیده
منابع مشابه
The Andrews-Curtis Conjecture and Black Box Groups
The paper discusses the Andrews-Curtis graph ∆k(G,N) of a normal subgroup N in a group G. The vertices of the graph are k-tuples of elements in N which generate N as a normal subgroup; two vertices are connected if one them can be obtained from another by certain elementary transformations. This object appears naturally in the theory of black box finite groups and in the Andrews-Curtis conjectu...
متن کاملAndrews-Curtis and Todd-Coxeter proof words
Andrews and Curtis have conjectured that every balanced presentation of the trivial group can be transformed into a standard presentation by a finite sequence of elementary transformations. It can be difficult to determine whether or not the conjecture holds for a particular presentation. We show that the utility PEACE, which produces proofs based on Todd-Coxeter coset enumeration, can produce ...
متن کاملOn the Andrews-Curtis equivalence
The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of \elementary transformations" which are Nielsen transformations augmented by arbitrary conjugations. It is a prevalent opinion that this conjecture is false; however, not many potential counterexamples are known. In this paper, we show that some of the pr...
متن کاملGenetic algorithms and the Andrews-Curtis conjecture
The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be transformed into the trivial presentation by a finite sequence of “elementary transformations” which are Nielsen transformations together with an arbitrary conjugation of a relator. It is believed that the Andrews-Curtis conjecture is false; however, not so many possible counterexamples are known. ...
متن کاملThe Finitary Andrews-Curtis Conjecture
The well known Andrews-Curtis Conjecture [2] is still open. In this paper, we establish its finite version by describing precisely the connected components of the Andrews-Curtis graphs of finite groups. This finite version has independent importance for computational group theory. It also resolves a question asked in [5] and shows that a computation in finite groups cannot lead to a counterexam...
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عنوان ژورنال:
- Experimental Mathematics
دوره 15 شماره
صفحات -
تاریخ انتشار 2006