| Title:
|
A note on infinite $aS$-groups (English) |
| Author:
|
Nikandish, Reza |
| Author:
|
Miraftab, Babak |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
65 |
| Issue:
|
4 |
| Year:
|
2015 |
| Pages:
|
1003-1009 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a group. If every nontrivial subgroup of $G$ has a proper supplement, then $G$ is called an $aS$-group. We study some properties of $aS$-groups. For instance, it is shown that a nilpotent group $G$ is an $aS$-group if and only if $G$ is a subdirect product of cyclic groups of prime orders. We prove that if $G$ is an $aS$-group which satisfies the descending chain condition on subgroups, then $G$ is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group is an $aS$-group. Finally, it is shown that if $G$ is an $aS$-group and $|G|\neq pq,p$, where $p$ and $q$ are primes, then $G$ has a triple factorization. (English) |
| Keyword:
|
infinite $aS$-group |
| Keyword:
|
supplemented subgroup |
| Keyword:
|
nilpotent group |
| MSC:
|
20E15 |
| MSC:
|
20E34 |
| MSC:
|
20F18 |
| idZBL:
|
Zbl 06537706 |
| idMR:
|
MR3441331 |
| DOI:
|
10.1007/s10587-015-0223-0 |
| . |
| Date available:
|
2016-01-13T09:14:08Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144788 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
