A Simple Classification of Finite Groups of Order p2q2
Suppose G is a group of order p2q2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p2q2 when Q and P are cyclic, three groups when Q is a cyclic...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Kashan
2018-12-01
|
| Series: | Mathematics Interdisciplinary Research |
| Subjects: | |
| Online Access: | https://mir.kashanu.ac.ir/article_45273_e39c942af529952ba55f29606887d4c6.pdf |
| _version_ | 1797630883572744192 |
|---|---|
| author | Aziz Seyyed Hadi Modjtaba Ghorbani Farzaneh Nowroozi Larki |
| author_facet | Aziz Seyyed Hadi Modjtaba Ghorbani Farzaneh Nowroozi Larki |
| author_sort | Aziz Seyyed Hadi |
| collection | DOAJ |
| description | Suppose G is a group of order p2q2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p2q2 when Q and P are cyclic, three groups when Q is a cyclic and P is an elementary ablian group, p2+3p/2+7 groups when Q is an elementary ablian group and P is a cyclic group and finally, p + 5 groups when both Q and P are elementary abelian groups. |
| first_indexed | 2024-03-11T11:13:14Z |
| format | Article |
| id | doaj.art-35943b9840044a7287c5bfc0b898406f |
| institution | Directory Open Access Journal |
| issn | 2476-4965 |
| language | English |
| last_indexed | 2024-03-11T11:13:14Z |
| publishDate | 2018-12-01 |
| publisher | University of Kashan |
| record_format | Article |
| series | Mathematics Interdisciplinary Research |
| spelling | doaj.art-35943b9840044a7287c5bfc0b898406f2023-11-11T08:10:21ZengUniversity of KashanMathematics Interdisciplinary Research2476-49652018-12-0132899810.22052/mir.2017.62726.104445273A Simple Classification of Finite Groups of Order p2q2Aziz Seyyed Hadi0Modjtaba Ghorbani1Farzaneh Nowroozi Larki2Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training UniversityDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training UniversityDepartment of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training UniversitySuppose G is a group of order p2q2 where p>q are prime numbers and suppose P and Q are Sylow p-subgroups and Sylow q-subgroups of G, respectively. In this paper, we show that up to isomorphism, there are four groups of order p2q2 when Q and P are cyclic, three groups when Q is a cyclic and P is an elementary ablian group, p2+3p/2+7 groups when Q is an elementary ablian group and P is a cyclic group and finally, p + 5 groups when both Q and P are elementary abelian groups.https://mir.kashanu.ac.ir/article_45273_e39c942af529952ba55f29606887d4c6.pdfsemi-direct productp-groupsylow subgroup |
| spellingShingle | Aziz Seyyed Hadi Modjtaba Ghorbani Farzaneh Nowroozi Larki A Simple Classification of Finite Groups of Order p2q2 Mathematics Interdisciplinary Research semi-direct product p-group sylow subgroup |
| title | A Simple Classification of Finite Groups of Order p2q2 |
| title_full | A Simple Classification of Finite Groups of Order p2q2 |
| title_fullStr | A Simple Classification of Finite Groups of Order p2q2 |
| title_full_unstemmed | A Simple Classification of Finite Groups of Order p2q2 |
| title_short | A Simple Classification of Finite Groups of Order p2q2 |
| title_sort | simple classification of finite groups of order p2q2 |
| topic | semi-direct product p-group sylow subgroup |
| url | https://mir.kashanu.ac.ir/article_45273_e39c942af529952ba55f29606887d4c6.pdf |
| work_keys_str_mv | AT azizseyyedhadi asimpleclassificationoffinitegroupsoforderp2q2 AT modjtabaghorbani asimpleclassificationoffinitegroupsoforderp2q2 AT farzanehnowroozilarki asimpleclassificationoffinitegroupsoforderp2q2 AT azizseyyedhadi simpleclassificationoffinitegroupsoforderp2q2 AT modjtabaghorbani simpleclassificationoffinitegroupsoforderp2q2 AT farzanehnowroozilarki simpleclassificationoffinitegroupsoforderp2q2 |