Some properties of n-capable and n-perfect groups
In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Mor...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Tehran
2013-12-01
|
| Series: | Journal of Sciences, Islamic Republic of Iran |
| Subjects: | |
| Online Access: | https://jsciences.ut.ac.ir/article_36457_52c4a08f484812fbb2c22163f5342e7b.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850270160685891584 |
|---|---|
| author | M. R. Rismanchian |
| author_facet | M. R. Rismanchian |
| author_sort | M. R. Rismanchian |
| collection | DOAJ |
| description | In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied. |
| format | Article |
| id | doaj-art-6d85799b993f454994c2ce5f1b763cc6 |
| institution | OA Journals |
| issn | 1016-1104 2345-6914 |
| language | English |
| publishDate | 2013-12-01 |
| publisher | University of Tehran |
| record_format | Article |
| series | Journal of Sciences, Islamic Republic of Iran |
| spelling | doaj-art-6d85799b993f454994c2ce5f1b763cc62025-08-20T01:52:45ZengUniversity of TehranJournal of Sciences, Islamic Republic of Iran1016-11042345-69142013-12-0124436136436457Some properties of n-capable and n-perfect groupsM. R. Rismanchian0Department of Pure Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord, Islamic Republic of Iran.In this article we introduce the notion of n-capable groups. It is shown that every group G admits a uniquely determined subgroup (〖Z^n)〗^* (G) which is a characteristic subgroup and lies in the n-centre subgroup of the group G. This is the smallest subgroup of G whose factor group is n-capable. Moreover, some properties of n-central extension will be studied.https://jsciences.ut.ac.ir/article_36457_52c4a08f484812fbb2c22163f5342e7b.pdfn-centraln-capablen-perfectn-unicentral |
| spellingShingle | M. R. Rismanchian Some properties of n-capable and n-perfect groups Journal of Sciences, Islamic Republic of Iran n-central n-capable n-perfect n-unicentral |
| title | Some properties of n-capable and n-perfect groups |
| title_full | Some properties of n-capable and n-perfect groups |
| title_fullStr | Some properties of n-capable and n-perfect groups |
| title_full_unstemmed | Some properties of n-capable and n-perfect groups |
| title_short | Some properties of n-capable and n-perfect groups |
| title_sort | some properties of n capable and n perfect groups |
| topic | n-central n-capable n-perfect n-unicentral |
| url | https://jsciences.ut.ac.ir/article_36457_52c4a08f484812fbb2c22163f5342e7b.pdf |
| work_keys_str_mv | AT mrrismanchian somepropertiesofncapableandnperfectgroups |