Infinite groups with many generalized normal subgroups
A subgroup $X$ of a group $G$ is almost normal if the index $|G:N_G(X)|$ is finite, while $X$ is nearly normal if it has finite index in the normal closure $X^G$. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
University of Isfahan
2012-09-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://www.theoryofgroups.ir/?_action=showPDF&article=1223&_ob=150426f6f6fcaf626f8a811ef1dd2718&fileName=full_text.pdf |
| _version_ | 1811194309966299136 |
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| author | Francesco de Giovanni Caterina Rainone |
| author_facet | Francesco de Giovanni Caterina Rainone |
| author_sort | Francesco de Giovanni |
| collection | DOAJ |
| description | A subgroup $X$ of a group $G$ is almost normal if the index $|G:N_G(X)|$ is finite, while $X$ is nearly normal if it has finite index in the normal closure $X^G$. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal. |
| first_indexed | 2024-04-12T00:24:55Z |
| format | Article |
| id | doaj.art-d001a161ed0f457bb6e6333b592ad41d |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-04-12T00:24:55Z |
| publishDate | 2012-09-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-d001a161ed0f457bb6e6333b592ad41d2022-12-22T03:55:35ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692012-09-01133949Infinite groups with many generalized normal subgroupsFrancesco de GiovanniCaterina RainoneA subgroup $X$ of a group $G$ is almost normal if the index $|G:N_G(X)|$ is finite, while $X$ is nearly normal if it has finite index in the normal closure $X^G$. This paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.http://www.theoryofgroups.ir/?_action=showPDF&article=1223&_ob=150426f6f6fcaf626f8a811ef1dd2718&fileName=full_text.pdfAlmost normalitynearly normalitynormalizer subgroup |
| spellingShingle | Francesco de Giovanni Caterina Rainone Infinite groups with many generalized normal subgroups International Journal of Group Theory Almost normality nearly normality normalizer subgroup |
| title | Infinite groups with many generalized normal subgroups |
| title_full | Infinite groups with many generalized normal subgroups |
| title_fullStr | Infinite groups with many generalized normal subgroups |
| title_full_unstemmed | Infinite groups with many generalized normal subgroups |
| title_short | Infinite groups with many generalized normal subgroups |
| title_sort | infinite groups with many generalized normal subgroups |
| topic | Almost normality nearly normality normalizer subgroup |
| url | http://www.theoryofgroups.ir/?_action=showPDF&article=1223&_ob=150426f6f6fcaf626f8a811ef1dd2718&fileName=full_text.pdf |
| work_keys_str_mv | AT francescodegiovanni infinitegroupswithmanygeneralizednormalsubgroups AT caterinarainone infinitegroupswithmanygeneralizednormalsubgroups |