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Andrews–Curtis conjecture : ウィキペディア英語版 | Andrews–Curtis conjecture In mathematics, the Andrews–Curtis conjecture states that every balanced presentation of the trivial group can be transformed into a trivial presentation by a sequence of Nielsen transformations on the relators together with conjugations of relators, named after James J. Andrews and Morton L. Curtis who proposed it in 1965. It is difficult to verify whether the conjecture holds for a given balanced presentation or not. It is widely believed that the Andrews–Curtis conjecture is false. While there are no counterexamples known, there are numerous potential counterexamples.〔(Open problems in combinatorial group theory )〕 It is known that the Zeeman conjecture on collapsibility implies the Andrews–Curtis conjecture. ==References==
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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Andrews–Curtis conjecture」の詳細全文を読む
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