Article
| Title: | Extending subgroup and subring isomorphisms to automorphisms (English) |
| Author: | Oman, Greg |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 3 |
| Year: | 2026 |
| Pages: | 747-762 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $G$ be an Abelian group. Then $G$ is called a $T_1'$ group provided that for every pair of isomorphic subgroups $H$ and $K$ of $G$ and every isomorphism $\varphi \colon H\to K$, $\varphi $ can be extended to an automorphism of $G$. Let us call $G$ a weakly $T_1'$ group if for any elements $a$ and $b$ of $G$ of the same order, there is an automorphism $\varphi \colon G\to G$ such that $\varphi (a)=b$. We determine both classes of groups, correcting a result in the literature. We then study several analogues for rings. (English) |
| Keyword: | automorphism |
| Keyword: | Boolean ring |
| Keyword: | divisible Abelian group |
| Keyword: | Galois ring |
| Keyword: | homococyclic group |
| Keyword: | injective hull |
| Keyword: | $p$-component |
| Keyword: | quasi-cyclic group |
| Keyword: | uniserial ring |
| MSC: | 16D50 |
| MSC: | 20K27 |
| MSC: | 20K30 |
| DOI: | 10.21136/CMJ.2026.0475-24 |
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| Date available: | 2026-09-11T13:10:28Z |
| Last updated: | 2026-09-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153726 |
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