The normalizer problem for finite groups having normal $ 2 $-complements
Assume that $ H $ is a finite group that has a normal $ 2 $-complement. Under some conditions, it is proven that the normalizer property holds for $ H $. In particular, if there is a nilpotent subgroup of index $ 2 $ in $ H $, then $ H $ has the normalizer property. The result of Li, Sehgal and Parm...
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AIMS Press
2024-08-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2024225 |
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| _version_ | 1832590819023912960 |
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| author | Jidong Guo Liang Zhang Jinke Hai |
| author_facet | Jidong Guo Liang Zhang Jinke Hai |
| author_sort | Jidong Guo |
| collection | DOAJ |
| description | Assume that $ H $ is a finite group that has a normal $ 2 $-complement. Under some conditions, it is proven that the normalizer property holds for $ H $. In particular, if there is a nilpotent subgroup of index $ 2 $ in $ H $, then $ H $ has the normalizer property. The result of Li, Sehgal and Parmenter, stating that the normalizer property holds for finite groups that have an abelian subgroup of index $ 2 $ is generalized. |
| format | Article |
| id | doaj-art-6cf9ef7d3dd34d798a3303d7922e3043 |
| institution | Kabale University |
| issn | 2688-1594 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-6cf9ef7d3dd34d798a3303d7922e30432025-01-23T07:51:27ZengAIMS PressElectronic Research Archive2688-15942024-08-013284905491210.3934/era.2024225The normalizer problem for finite groups having normal $ 2 $-complementsJidong Guo0Liang Zhang1Jinke Hai2College of Mathematics and Statistics, Yili Normal University, Yining 835000, ChinaCollege of Mathematics and Statistics, Yili Normal University, Yining 835000, ChinaCollege of Mathematics and Statistics, Yili Normal University, Yining 835000, ChinaAssume that $ H $ is a finite group that has a normal $ 2 $-complement. Under some conditions, it is proven that the normalizer property holds for $ H $. In particular, if there is a nilpotent subgroup of index $ 2 $ in $ H $, then $ H $ has the normalizer property. The result of Li, Sehgal and Parmenter, stating that the normalizer property holds for finite groups that have an abelian subgroup of index $ 2 $ is generalized.https://www.aimspress.com/article/doi/10.3934/era.2024225the normalizer propertycoleman automorphismsclass-preserving automorphismsnormal $ 2 $-complements |
| spellingShingle | Jidong Guo Liang Zhang Jinke Hai The normalizer problem for finite groups having normal $ 2 $-complements Electronic Research Archive the normalizer property coleman automorphisms class-preserving automorphisms normal $ 2 $-complements |
| title | The normalizer problem for finite groups having normal $ 2 $-complements |
| title_full | The normalizer problem for finite groups having normal $ 2 $-complements |
| title_fullStr | The normalizer problem for finite groups having normal $ 2 $-complements |
| title_full_unstemmed | The normalizer problem for finite groups having normal $ 2 $-complements |
| title_short | The normalizer problem for finite groups having normal $ 2 $-complements |
| title_sort | normalizer problem for finite groups having normal 2 complements |
| topic | the normalizer property coleman automorphisms class-preserving automorphisms normal $ 2 $-complements |
| url | https://www.aimspress.com/article/doi/10.3934/era.2024225 |
| work_keys_str_mv | AT jidongguo thenormalizerproblemforfinitegroupshavingnormal2complements AT liangzhang thenormalizerproblemforfinitegroupshavingnormal2complements AT jinkehai thenormalizerproblemforfinitegroupshavingnormal2complements AT jidongguo normalizerproblemforfinitegroupshavingnormal2complements AT liangzhang normalizerproblemforfinitegroupshavingnormal2complements AT jinkehai normalizerproblemforfinitegroupshavingnormal2complements |