自由群与带状集上自由幂等生成半群的直积
群论
2013-03-26 v3
摘要
对于每个可分解为有限秩自由群有限直积的群 G，我们构造一个正则带 B，使得 B 上的自由幂等生成半群包含一个同构于 G 的最大子群。特别地，存在一个（正则）带 B_0，使得任何幂等生成半群，只要其双序集同构于 B_0 的双序集，其所有子群必为阿贝尔群。
引用
@article{arxiv.1109.4402,
title = {Direct products of free groups and free idempotent generated semigroups over bands},
author = {Igor Dolinka},
journal= {arXiv preprint arXiv:1109.4402},
year = {2013}
}
备注
The paper is rendered practically meaningless by arXiv:1301.1225 (accepted for publication in the meantime) since the latter proves a result which is substantially more general, as opposed to the partial, piecemeal result contained in the present note