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).
@article{1377,
title = {Some New Characterizations for PGL(2, q)},
journal = {CUBO, A Mathematical Journal},
volume = {13},
year = {2011},
language = {en},
url = {http://dml.mathdoc.fr/item/1377}
}
Khosravi, B.; Khatami, M.; Akhlaghi, Z. Some New Characterizations for PGL(2, q). CUBO, A Mathematical Journal, Tome 13 (2011) . http://gdmltest.u-ga.fr/item/1377/