| Title:
|
On the lattice of pronormal subgroups of dicyclic, alternating and symmetric groups (English) |
| Author:
|
Mitkari, Shrawani |
| Author:
|
Kharat, Vilas |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
3 |
| Year:
|
2024 |
| Pages:
|
427-438 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, the structures of collection of pronormal subgroups of dicyclic, symmetric and alternating groups $G$ are studied in respect of formation of lattices ${\rm L}(G)$ and sublattices of ${\rm L}(G)$. It is proved that the collections of all pronormal subgroups of ${\rm A}_n$ and S$_n$ do not form sublattices of respective ${\rm L}({\rm A}_n)$ and ${\rm L}({\rm S}_n)$, whereas the collection of all pronormal subgroups ${\rm LPrN}({\rm Dic}_n)$ of a dicyclic group is a sublattice of ${\rm L}({\rm Dic}_n)$. Furthermore, it is shown that ${\rm L}({\rm Dic}_n)$ and ${\rm LPrN}({\rm Dic}_n$) are lower semimodular lattices. (English) |
| Keyword:
|
alternating group |
| Keyword:
|
dicyclic group |
| Keyword:
|
pronormal subgroup |
| Keyword:
|
lattice of subgroups |
| Keyword:
|
lower semimodular lattice |
| MSC:
|
06A06 |
| MSC:
|
06A07 |
| MSC:
|
06B20 |
| MSC:
|
06B23 |
| MSC:
|
20D25 |
| MSC:
|
20D30 |
| MSC:
|
20D40 |
| MSC:
|
20E15 |
| MSC:
|
20F22 |
| MSC:
|
20K27 |
| DOI:
|
10.21136/MB.2023.0146-22 |
| . |
| Date available:
|
2024-09-11T13:49:39Z |
| Last updated:
|
2024-09-11 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152543 |
| . |
| 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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| Reference:
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| Reference:
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