On maximal subgroups of free idempotent generated semigroups
On maximal subgroups of free idempotent generated semigroups
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DOI：
10.1007/s11856-011-0154-x
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发表时间：
2011-09
影响因子：
1
通讯作者：
R. Gray;N. Ruškuc
中科院分区：
文献类型：
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作者：
R. Gray;N. Ruškuc
证明了如下结果：（1）每个群都是某个自由幂等元生成半群的极大子群。(2)每一个可表示群都是由有限半群生成的自由幂等元生成半群的极大子群。(3)每个群都是某个自由正则幂等元生成半群的极大子群。(4)每个有限群都是由有限正则半群生成的自由正则幂等元生成半群的极大子群。作为这些结果的一个技术前提，我们建立了一个一般的介绍，基于Reidemeister-Schreier型重写的极大子群。
We prove the following results: (1) Every group is a maximal subgroup of some free idempotent generated semigroup. (2) Every finitely presented group is a maximal subgroup of some free idempotent generated semigroup arising from a finite semigroup. (3) Every group is a maximal subgroup of some free regular idempotent generated semigroup. (4) Every finite group is a maximal subgroup of some free regular idempotent generated semigroup arising from a finite regular semigroup. As a technical prerequisite for these results we establish a general presentation for the maximal subgroups based on a Reidemeister-Schreier type rewriting.