Some New Characterizations for PGL(2, q)
Many authors introduced some characterizations for finite groups. In this paper as the main result we prove that the finite group PGL(2, q) is uniquely determined by its noncommuting graph. Also we prove that PGL(2, q) is characterizable by its noncyclic graph. Throughout the proof of these results...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universidad de La Frontera
2011-06-01
|
| Series: | Cubo |
| Subjects: | |
| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000200009 |
| _version_ | 1818913166175764480 |
|---|---|
| author | B Khosravi M Khatami Z Akhlaghi |
| author_facet | B Khosravi M Khatami Z Akhlaghi |
| author_sort | B Khosravi |
| collection | DOAJ |
| description | Many authors introduced some characterizations for finite groups. In this paper as the main result we prove that the finite group PGL(2, q) is uniquely determined by its noncommuting graph. Also we prove that PGL(2, q) is characterizable by its noncyclic graph. Throughout the proof of these results we prove that PGL(2, q) is uniquely determined by its order components and using this fact we give positive answer to a conjecture of Thompson and another conjecture of Shi and Bi for the group PGL(2, q).<br>Muchos autores introdujeron algunas caracterizaciones de los grupos finitos. En este trabajo como principal resultado se demuestra que grupo finito PGL(2, q) es determinado nicamente por su gráfica no conmutativa. También se demuestra que PGL(2, q) es caracterizable por su gráfico no cíclico. A lo largo de la prueba de estos resultados se demuestra que PGL(2,Q) es determinado únicamente por los componentes de su orden y con ello damos respuesta positiva a una conjetura de Thompson y otra conjetura de Shi Bi y para el grupo PGL(2, q) |
| first_indexed | 2024-12-19T23:26:10Z |
| format | Article |
| id | doaj.art-d49d5d8304da463cada56e147082313d |
| institution | Directory Open Access Journal |
| issn | 0716-7776 0719-0646 |
| language | English |
| last_indexed | 2024-12-19T23:26:10Z |
| publishDate | 2011-06-01 |
| publisher | Universidad de La Frontera |
| record_format | Article |
| series | Cubo |
| spelling | doaj.art-d49d5d8304da463cada56e147082313d2022-12-21T20:01:51ZengUniversidad de La FronteraCubo0716-77760719-06462011-06-01132151161Some New Characterizations for PGL(2, q)B KhosraviM KhatamiZ AkhlaghiMany authors introduced some characterizations for finite groups. In this paper as the main result we prove that the finite group PGL(2, q) is uniquely determined by its noncommuting graph. Also we prove that PGL(2, q) is characterizable by its noncyclic graph. Throughout the proof of these results we prove that PGL(2, q) is uniquely determined by its order components and using this fact we give positive answer to a conjecture of Thompson and another conjecture of Shi and Bi for the group PGL(2, q).<br>Muchos autores introdujeron algunas caracterizaciones de los grupos finitos. En este trabajo como principal resultado se demuestra que grupo finito PGL(2, q) es determinado nicamente por su gráfica no conmutativa. También se demuestra que PGL(2, q) es caracterizable por su gráfico no cíclico. A lo largo de la prueba de estos resultados se demuestra que PGL(2,Q) es determinado únicamente por los componentes de su orden y con ello damos respuesta positiva a una conjetura de Thompson y otra conjetura de Shi Bi y para el grupo PGL(2, q)http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000200009Noncommuting graphprime graphnoncyclic graphorder components |
| spellingShingle | B Khosravi M Khatami Z Akhlaghi Some New Characterizations for PGL(2, q) Cubo Noncommuting graph prime graph noncyclic graph order components |
| title | Some New Characterizations for PGL(2, q) |
| title_full | Some New Characterizations for PGL(2, q) |
| title_fullStr | Some New Characterizations for PGL(2, q) |
| title_full_unstemmed | Some New Characterizations for PGL(2, q) |
| title_short | Some New Characterizations for PGL(2, q) |
| title_sort | some new characterizations for pgl 2 q |
| topic | Noncommuting graph prime graph noncyclic graph order components |
| url | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000200009 |
| work_keys_str_mv | AT bkhosravi somenewcharacterizationsforpgl2q AT mkhatami somenewcharacterizationsforpgl2q AT zakhlaghi somenewcharacterizationsforpgl2q |