A group and the completion of its coset semigroup
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916543610224640 |
|---|---|
| author | Zhao, Xian-zhong Gao, Zi-dong Lei, Dong-lin |
| author_facet | Zhao, Xian-zhong Gao, Zi-dong Lei, Dong-lin |
| contents | Let ${\cal K}_1(G)$ denote the inverse subsemigroup of ${\cal K}(G)$ consisting of all right cosets of all non-trivial subgroups of $G$. This paper concentrates on the study of the group $Σ({\cal K}_1(G))$ of all units of the completion of ${\cal K}_1(G)$. The characterizations and the representations of $Σ({\cal K}_1(G))$ are given when $G$ is a periodic group whose minimal subgroups permute with each other. Based on these, for such groups $G$ except some special $p$-groups, it is shown that $G$ and its coset semigroup ${\cal K}_1(G)$ are uniquely determined by each other, up to isomorphism. This extends the related results obtained by Schein in 1973. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19486 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A group and the completion of its coset semigroup Zhao, Xian-zhong Gao, Zi-dong Lei, Dong-lin Group Theory Let ${\cal K}_1(G)$ denote the inverse subsemigroup of ${\cal K}(G)$ consisting of all right cosets of all non-trivial subgroups of $G$. This paper concentrates on the study of the group $Σ({\cal K}_1(G))$ of all units of the completion of ${\cal K}_1(G)$. The characterizations and the representations of $Σ({\cal K}_1(G))$ are given when $G$ is a periodic group whose minimal subgroups permute with each other. Based on these, for such groups $G$ except some special $p$-groups, it is shown that $G$ and its coset semigroup ${\cal K}_1(G)$ are uniquely determined by each other, up to isomorphism. This extends the related results obtained by Schein in 1973. |
| title | A group and the completion of its coset semigroup |
| topic | Group Theory |
| url | https://arxiv.org/abs/2412.19486 |