Eintrag weiter verarbeiten
Some New Applications of Weakly H-Embedded Subgroups of Finite Groups
Gespeichert in:
| Zeitschriftentitel: | Mathematics |
|---|---|
| Personen und Körperschaften: | , , |
| In: | Mathematics, 7, 2019, 2, S. 158 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
MDPI AG
|
| Schlagwörter: |
| author_facet |
Zhang, Li Huo, Li-Jun Liu, Jia-Bao Zhang, Li Huo, Li-Jun Liu, Jia-Bao |
|---|---|
| author |
Zhang, Li Huo, Li-Jun Liu, Jia-Bao |
| spellingShingle |
Zhang, Li Huo, Li-Jun Liu, Jia-Bao Mathematics Some New Applications of Weakly H-Embedded Subgroups of Finite Groups General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) |
| author_sort |
zhang, li |
| spelling |
Zhang, Li Huo, Li-Jun Liu, Jia-Bao 2227-7390 MDPI AG General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) http://dx.doi.org/10.3390/math7020158 <jats:p>A subgroup H of a finite group G is said to be weakly H -embedded in G if there exists a normal subgroup T of G such that H G = H T and H ∩ T ∈ H ( G ) , where H G is the normal closure of H in G, and H ( G ) is the set of all H -subgroups of G. In the recent research, Asaad, Ramadan and Heliel gave new characterization of p-nilpotent: Let p be the smallest prime dividing | G | , and P a non-cyclic Sylow p-subgroup of G. Then G is p-nilpotent if and only if there exists a p-power d with 1 < d < | P | such that all subgroups of P of order d and p d are weakly H -embedded in G. As new applications of weakly H -embedded subgroups, in this paper, (1) we generalize this result for general prime p and get a new criterion for p-supersolubility; (2) adding the condition “ N G ( P ) is p-nilpotent”, here N G ( P ) = { g ∈ G | P g = P } is the normalizer of P in G, we obtain p-nilpotence for general prime p. Moreover, our tool is the weakly H -embedded subgroup. However, instead of the normality of H G = H T , we just need H T is S-quasinormal in G, which means that H T permutes with every Sylow subgroup of G.</jats:p> Some New Applications of Weakly H-Embedded Subgroups of Finite Groups Mathematics |
| doi_str_mv |
10.3390/math7020158 |
| facet_avail |
Online Free |
| finc_class_facet |
Technik Informatik |
| format |
ElectronicArticle |
| fullrecord |
blob:ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMzM5MC9tYXRoNzAyMDE1OA |
| id |
ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMzM5MC9tYXRoNzAyMDE1OA |
| institution |
DE-Bn3 DE-Brt1 DE-Zwi2 DE-D161 DE-Gla1 DE-Zi4 DE-15 DE-Pl11 DE-Rs1 DE-105 DE-14 DE-Ch1 DE-L229 DE-D275 |
| imprint |
MDPI AG, 2019 |
| imprint_str_mv |
MDPI AG, 2019 |
| issn |
2227-7390 |
| issn_str_mv |
2227-7390 |
| language |
English |
| mega_collection |
MDPI AG (CrossRef) |
| match_str |
zhang2019somenewapplicationsofweaklyhembeddedsubgroupsoffinitegroups |
| publishDateSort |
2019 |
| publisher |
MDPI AG |
| recordtype |
ai |
| record_format |
ai |
| series |
Mathematics |
| source_id |
49 |
| title |
Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_unstemmed |
Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_full |
Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_fullStr |
Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_full_unstemmed |
Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_short |
Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_sort |
some new applications of weakly h-embedded subgroups of finite groups |
| topic |
General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) |
| url |
http://dx.doi.org/10.3390/math7020158 |
| publishDate |
2019 |
| physical |
158 |
| description |
<jats:p>A subgroup H of a finite group G is said to be weakly H -embedded in G if there exists a normal subgroup T of G such that H G = H T and H ∩ T ∈ H ( G ) , where H G is the normal closure of H in G, and H ( G ) is the set of all H -subgroups of G. In the recent research, Asaad, Ramadan and Heliel gave new characterization of p-nilpotent: Let p be the smallest prime dividing | G | , and P a non-cyclic Sylow p-subgroup of G. Then G is p-nilpotent if and only if there exists a p-power d with 1 < d < | P | such that all subgroups of P of order d and p d are weakly H -embedded in G. As new applications of weakly H -embedded subgroups, in this paper, (1) we generalize this result for general prime p and get a new criterion for p-supersolubility; (2) adding the condition “ N G ( P ) is p-nilpotent”, here N G ( P ) = { g ∈ G | P g = P } is the normalizer of P in G, we obtain p-nilpotence for general prime p. Moreover, our tool is the weakly H -embedded subgroup. However, instead of the normality of H G = H T , we just need H T is S-quasinormal in G, which means that H T permutes with every Sylow subgroup of G.</jats:p> |
| container_issue |
2 |
| container_start_page |
0 |
| container_title |
Mathematics |
| container_volume |
7 |
| format_de105 |
Article, E-Article |
| format_de14 |
Article, E-Article |
| format_de15 |
Article, E-Article |
| format_de520 |
Article, E-Article |
| format_de540 |
Article, E-Article |
| format_dech1 |
Article, E-Article |
| format_ded117 |
Article, E-Article |
| format_degla1 |
E-Article |
| format_del152 |
Buch |
| format_del189 |
Article, E-Article |
| format_dezi4 |
Article |
| format_dezwi2 |
Article, E-Article |
| format_finc |
Article, E-Article |
| format_nrw |
Article, E-Article |
| _version_ |
1792326015714852871 |
| geogr_code |
not assigned |
| last_indexed |
2024-03-01T12:14:47.5Z |
| geogr_code_person |
not assigned |
| openURL |
url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fvufind.svn.sourceforge.net%3Agenerator&rft.title=Some+New+Applications+of+Weakly+H-Embedded+Subgroups+of+Finite+Groups&rft.date=2019-02-10&genre=article&issn=2227-7390&volume=7&issue=2&pages=158&jtitle=Mathematics&atitle=Some+New+Applications+of+Weakly+H-Embedded+Subgroups+of+Finite+Groups&aulast=Liu&aufirst=Jia-Bao&rft_id=info%3Adoi%2F10.3390%2Fmath7020158&rft.language%5B0%5D=eng |
| SOLR | |
| _version_ | 1792326015714852871 |
| author | Zhang, Li, Huo, Li-Jun, Liu, Jia-Bao |
| author_facet | Zhang, Li, Huo, Li-Jun, Liu, Jia-Bao, Zhang, Li, Huo, Li-Jun, Liu, Jia-Bao |
| author_sort | zhang, li |
| container_issue | 2 |
| container_start_page | 0 |
| container_title | Mathematics |
| container_volume | 7 |
| description | <jats:p>A subgroup H of a finite group G is said to be weakly H -embedded in G if there exists a normal subgroup T of G such that H G = H T and H ∩ T ∈ H ( G ) , where H G is the normal closure of H in G, and H ( G ) is the set of all H -subgroups of G. In the recent research, Asaad, Ramadan and Heliel gave new characterization of p-nilpotent: Let p be the smallest prime dividing | G | , and P a non-cyclic Sylow p-subgroup of G. Then G is p-nilpotent if and only if there exists a p-power d with 1 < d < | P | such that all subgroups of P of order d and p d are weakly H -embedded in G. As new applications of weakly H -embedded subgroups, in this paper, (1) we generalize this result for general prime p and get a new criterion for p-supersolubility; (2) adding the condition “ N G ( P ) is p-nilpotent”, here N G ( P ) = { g ∈ G | P g = P } is the normalizer of P in G, we obtain p-nilpotence for general prime p. Moreover, our tool is the weakly H -embedded subgroup. However, instead of the normality of H G = H T , we just need H T is S-quasinormal in G, which means that H T permutes with every Sylow subgroup of G.</jats:p> |
| doi_str_mv | 10.3390/math7020158 |
| facet_avail | Online, Free |
| finc_class_facet | Technik, Informatik |
| format | ElectronicArticle |
| format_de105 | Article, E-Article |
| format_de14 | Article, E-Article |
| format_de15 | Article, E-Article |
| format_de520 | Article, E-Article |
| format_de540 | Article, E-Article |
| format_dech1 | Article, E-Article |
| format_ded117 | Article, E-Article |
| format_degla1 | E-Article |
| format_del152 | Buch |
| format_del189 | Article, E-Article |
| format_dezi4 | Article |
| format_dezwi2 | Article, E-Article |
| format_finc | Article, E-Article |
| format_nrw | Article, E-Article |
| geogr_code | not assigned |
| geogr_code_person | not assigned |
| id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMzM5MC9tYXRoNzAyMDE1OA |
| imprint | MDPI AG, 2019 |
| imprint_str_mv | MDPI AG, 2019 |
| institution | DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161, DE-Gla1, DE-Zi4, DE-15, DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275 |
| issn | 2227-7390 |
| issn_str_mv | 2227-7390 |
| language | English |
| last_indexed | 2024-03-01T12:14:47.5Z |
| match_str | zhang2019somenewapplicationsofweaklyhembeddedsubgroupsoffinitegroups |
| mega_collection | MDPI AG (CrossRef) |
| physical | 158 |
| publishDate | 2019 |
| publishDateSort | 2019 |
| publisher | MDPI AG |
| record_format | ai |
| recordtype | ai |
| series | Mathematics |
| source_id | 49 |
| spelling | Zhang, Li Huo, Li-Jun Liu, Jia-Bao 2227-7390 MDPI AG General Mathematics Engineering (miscellaneous) Computer Science (miscellaneous) http://dx.doi.org/10.3390/math7020158 <jats:p>A subgroup H of a finite group G is said to be weakly H -embedded in G if there exists a normal subgroup T of G such that H G = H T and H ∩ T ∈ H ( G ) , where H G is the normal closure of H in G, and H ( G ) is the set of all H -subgroups of G. In the recent research, Asaad, Ramadan and Heliel gave new characterization of p-nilpotent: Let p be the smallest prime dividing | G | , and P a non-cyclic Sylow p-subgroup of G. Then G is p-nilpotent if and only if there exists a p-power d with 1 < d < | P | such that all subgroups of P of order d and p d are weakly H -embedded in G. As new applications of weakly H -embedded subgroups, in this paper, (1) we generalize this result for general prime p and get a new criterion for p-supersolubility; (2) adding the condition “ N G ( P ) is p-nilpotent”, here N G ( P ) = { g ∈ G | P g = P } is the normalizer of P in G, we obtain p-nilpotence for general prime p. Moreover, our tool is the weakly H -embedded subgroup. However, instead of the normality of H G = H T , we just need H T is S-quasinormal in G, which means that H T permutes with every Sylow subgroup of G.</jats:p> Some New Applications of Weakly H-Embedded Subgroups of Finite Groups Mathematics |
| spellingShingle | Zhang, Li, Huo, Li-Jun, Liu, Jia-Bao, Mathematics, Some New Applications of Weakly H-Embedded Subgroups of Finite Groups, General Mathematics, Engineering (miscellaneous), Computer Science (miscellaneous) |
| title | Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_full | Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_fullStr | Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_full_unstemmed | Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_short | Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| title_sort | some new applications of weakly h-embedded subgroups of finite groups |
| title_unstemmed | Some New Applications of Weakly H-Embedded Subgroups of Finite Groups |
| topic | General Mathematics, Engineering (miscellaneous), Computer Science (miscellaneous) |
| url | http://dx.doi.org/10.3390/math7020158 |