Real Elements and p-Nilpotence of Finite Groups
Our first main result proves that every element of order 4 of a Sylow 2-subgroup S of a minimal non-2-nilpotent group G, is a real element of S. This allows to give a character-free proof of a theorem due to Isaacs and Navarro (see [9, Theorem B]). As an application, the authors show a common extens...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Aracne
2016-12-01
|
| Series: | Advances in Group Theory and Applications |
| Subjects: | |
| Online Access: | http://www.advgrouptheory.com/journal/Volumes/2/Ballester-Bolinches,%20Esteban-Romero,%20Ezquerro%20-%20Real%20elements%20and%20p-nilpotence%20of%20finite%20groups.pdf |
| _version_ | 1811209886845894656 |
|---|---|
| author | Adolfo Ballester-Bolinches Ramón Esteban-Romero Luis M. Ezquerro |
| author_facet | Adolfo Ballester-Bolinches Ramón Esteban-Romero Luis M. Ezquerro |
| author_sort | Adolfo Ballester-Bolinches |
| collection | DOAJ |
| description | Our first main result proves that every element of order 4 of a Sylow 2-subgroup S of a minimal non-2-nilpotent group G, is a real element of S. This allows to give a character-free proof of a theorem due to Isaacs and Navarro (see [9, Theorem B]). As an application, the authors show a common extension of the p-nilpotence criteria proved in [3] and [9]. |
| first_indexed | 2024-04-12T04:46:38Z |
| format | Article |
| id | doaj.art-2d7de8955c6f40c281c574848da386e4 |
| institution | Directory Open Access Journal |
| issn | 2499-1287 2499-1287 |
| language | English |
| last_indexed | 2024-04-12T04:46:38Z |
| publishDate | 2016-12-01 |
| publisher | Aracne |
| record_format | Article |
| series | Advances in Group Theory and Applications |
| spelling | doaj.art-2d7de8955c6f40c281c574848da386e42022-12-22T03:47:27ZengAracneAdvances in Group Theory and Applications2499-12872499-12872016-12-012253010.4399/97888548970143Real Elements and p-Nilpotence of Finite GroupsAdolfo Ballester-Bolinches0Ramón Esteban-Romero1Luis M. Ezquerro2Universitat de ValènciaUniversitat de ValènciaUniversidad Pública de NavarraOur first main result proves that every element of order 4 of a Sylow 2-subgroup S of a minimal non-2-nilpotent group G, is a real element of S. This allows to give a character-free proof of a theorem due to Isaacs and Navarro (see [9, Theorem B]). As an application, the authors show a common extension of the p-nilpotence criteria proved in [3] and [9].http://www.advgrouptheory.com/journal/Volumes/2/Ballester-Bolinches,%20Esteban-Romero,%20Ezquerro%20-%20Real%20elements%20and%20p-nilpotence%20of%20finite%20groups.pdfnormal p-complementcontrol of fusion |
| spellingShingle | Adolfo Ballester-Bolinches Ramón Esteban-Romero Luis M. Ezquerro Real Elements and p-Nilpotence of Finite Groups Advances in Group Theory and Applications normal p-complement control of fusion |
| title | Real Elements and p-Nilpotence of Finite Groups |
| title_full | Real Elements and p-Nilpotence of Finite Groups |
| title_fullStr | Real Elements and p-Nilpotence of Finite Groups |
| title_full_unstemmed | Real Elements and p-Nilpotence of Finite Groups |
| title_short | Real Elements and p-Nilpotence of Finite Groups |
| title_sort | real elements and p nilpotence of finite groups |
| topic | normal p-complement control of fusion |
| url | http://www.advgrouptheory.com/journal/Volumes/2/Ballester-Bolinches,%20Esteban-Romero,%20Ezquerro%20-%20Real%20elements%20and%20p-nilpotence%20of%20finite%20groups.pdf |
| work_keys_str_mv | AT adolfoballesterbolinches realelementsandpnilpotenceoffinitegroups AT ramonestebanromero realelementsandpnilpotenceoffinitegroups AT luismezquerro realelementsandpnilpotenceoffinitegroups |