Coset Enumeration in a Finitely Presented Semigroup
Coset Enumeration in a Finitely Presented Semigroup
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有限呈现半群中的陪集枚举
DOI：
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发表时间：
1978
期刊：
影响因子：
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通讯作者：
A. Jura
中科院分区：
文献类型：
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作者：
A. Jura
有限群的计数方法，即所谓的Todd-Coxeter过程，在[2]，[3]中已有描述。Leech [4]和Trotter [5]在计算机上实现了群的陪集计数过程。然而门德尔松[1]是第一个提出了一个正式的事实证明，这一过程结束后，有限的步骤，它实际上列举陪集在一个组。Dietze和Schaps [7]利用Todd-Coxeter方法求出了群中给定有限指数的所有子群. B。H. Neumann [8]对Todd-Coxeter方法进行了改进，使其能在半群中计数陪集，但没有证明该方法的有效性，也没有证明它能在半群中计数陪集.
The enumeration method for finite groups, the so-called Todd-Coxeter process, has been described in [2], [3]. Leech [4] and Trotter [5] carried out the process of coset enumeration for groups on a computer. However Mendelsohn [1] was the first to present a formal proof of the fact that this process ends after a finite number of steps and that it actually enumerates cosets in a group. Dietze and Schaps [7] used Todd-Coxeter′s method to find all subgroups of a given finite index in a finitely presented group. B. H. Neumann [8] modified Todd-Coxeter′s method to enumerate cosets in a semigroup, giving however no proofs of the effectiveness of this method nor that it actually enumerates cosets in a semigroup.