论文标题
有限呈现的特殊逆肌的最大亚组
Maximal subgroups of finitely presented special inverse monoids
论文作者
论文摘要
我们研究了有限呈现的特殊逆小膜的最大亚组（也称为$ \ Mathcal {h} $ - 类）。我们表明，在这种单体中可能出现的最大亚组正是递归呈现的组，此外，在$ e $单独的情况下也可能出现这样的最大亚组。我们还证明，可能的单位组恰好是有限生成的递归呈现的组。这改善了第一作者和鲁什库克的问题的结果并回答了问题。这些结果给出了对此类单元超出此类单元的最大亚组的第一个重要洞察力，并且结果共同表明，亚组结构有可能具有显着超过单元组的复杂性。我们还观察到，有限呈现的特殊逆反向单体（即使是$ e $ $ $）可能具有无限的许多成对非同构最大亚组。
We study the maximal subgroups (also known as group $\mathcal{H}$-classes) of finitely presented special inverse monoids. We show that the maximal subgroups which can arise in such monoids are exactly the recursively presented groups, and moreover every such maximal subgroup can also arise in the $E$-unitary case. We also prove that the possible groups of units are exactly the finitely generated recursively presented groups; this improves upon a result of, and answers a question of, the first author and Ruškuc. These results give the first significant insight into the maximal subgroups of such monoids beyond the group of units, and the results together demonstrate that it is possible for the subgroup structure to have a complexity which significantly exceeds that of the group of units. We also observe that a finitely presented special inverse monoid (even an $E$-unitary one) may have infinitely many pairwise non-isomorphic maximal subgroups.
