Supersolube subgroups
A subgroup H of a group G is termed permutable (or quasi normal) in G if it satisfies the following equivalent conditions: For any subgroup K of G, HK (the product of subgroups H and K) is a group. For any subgroup K of G, HK= KH, i.e., H and K are permuting subgroups. For every g in G, H permutes...
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| Format: | Article |
| Language: | English |
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Accademia Piceno Aprutina dei Velati
2020-06-01
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| Series: | Ratio Mathematica |
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| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/503 |
| _version_ | 1818116938756259840 |
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| author | Behnam Razzagh |
| author_facet | Behnam Razzagh |
| author_sort | Behnam Razzagh |
| collection | DOAJ |
| description | A subgroup H of a group G is termed permutable (or quasi normal) in G if it satisfies the following equivalent conditions:
For any subgroup K of G, HK (the product of subgroups H and K) is a group. For any subgroup K of G, HK= KH, i.e., H and K are permuting subgroups. For every g in G, H permutes with the cyclic subgroup generated by g. Also we say that G=AB is the mutually permutable product of the subgroups A and B if A permutes with every subgroup of B and B permutes with every subgroup of A. We say that the product is totally permutable if every subgroup of A permutes with every subgroup of B. In this paper we prove the following theorem.
Let G=AB be the mutually permutable product of the super soluble subgroups A and B. If CoreG(A∩B)=1, then G is super soluble. |
| first_indexed | 2024-12-11T04:30:28Z |
| format | Article |
| id | doaj.art-a1d628e221654fd387833adfd73194a8 |
| institution | Directory Open Access Journal |
| issn | 1592-7415 2282-8214 |
| language | English |
| last_indexed | 2024-12-11T04:30:28Z |
| publishDate | 2020-06-01 |
| publisher | Accademia Piceno Aprutina dei Velati |
| record_format | Article |
| series | Ratio Mathematica |
| spelling | doaj.art-a1d628e221654fd387833adfd73194a82022-12-22T01:20:53ZengAccademia Piceno Aprutina dei VelatiRatio Mathematica1592-74152282-82142020-06-0138038539310.23755/rm.v38i0.503473Supersolube subgroupsBehnam Razzagh0Islamic Azad University Talesh branch. Talesh, Iran.A subgroup H of a group G is termed permutable (or quasi normal) in G if it satisfies the following equivalent conditions: For any subgroup K of G, HK (the product of subgroups H and K) is a group. For any subgroup K of G, HK= KH, i.e., H and K are permuting subgroups. For every g in G, H permutes with the cyclic subgroup generated by g. Also we say that G=AB is the mutually permutable product of the subgroups A and B if A permutes with every subgroup of B and B permutes with every subgroup of A. We say that the product is totally permutable if every subgroup of A permutes with every subgroup of B. In this paper we prove the following theorem. Let G=AB be the mutually permutable product of the super soluble subgroups A and B. If CoreG(A∩B)=1, then G is super soluble.http://eiris.it/ojs/index.php/ratiomathematica/article/view/503quasinormalpermutable productsuper soluble |
| spellingShingle | Behnam Razzagh Supersolube subgroups Ratio Mathematica quasinormal permutable product super soluble |
| title | Supersolube subgroups |
| title_full | Supersolube subgroups |
| title_fullStr | Supersolube subgroups |
| title_full_unstemmed | Supersolube subgroups |
| title_short | Supersolube subgroups |
| title_sort | supersolube subgroups |
| topic | quasinormal permutable product super soluble |
| url | http://eiris.it/ojs/index.php/ratiomathematica/article/view/503 |
| work_keys_str_mv | AT behnamrazzagh supersolubesubgroups |