Coclass theory for nilpotent semigroups via their associated algebras
Coclass theory for nilpotent semigroups via their associated algebras
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DOI：
10.1016/j.jalgebra.2012.09.042
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发表时间：
2012-08
影响因子：
0.9
通讯作者：
A. Distler;B. Eick
中科院分区：
文献类型：
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作者：
A. Distler;B. Eick
共类理论是研究有限幂零群和分类的一种非常成功的方法。本文提出了对有限幂零半群的一种改进：研究幂零半群的缩半群代数的协类图。我们展示了一系列关于这些协类图形状的猜想。如果这些被证明，那么这就把一个固定协类的幂零半群的分类简化为一个有限计算。我们证明了我们的猜想是由余类0和余类1的幂零半群支持的。计算实验表明，这些猜想也适用于coclass 2和coclass 3的幂零半群。
Coclass theory has been a highly successful approach towards the investigation and classification of finite nilpotent groups. Here we suggest a variation of this approach for finite nilpotent semigroups: we propose to study coclass graphs for the contracted semigroup algebras of nilpotent semigroups. We exhibit a series of conjectures on the shape of these coclass graphs. If these are proven, then this reduces the classification of nilpotent semigroups of a fixed coclass to a finite calculation. We show that our conjectures are supported by the nilpotent semigroups of coclass 0 and 1. Computational experiments suggest that the conjectures also hold for the nilpotent semigroups of coclass 2 and 3.