{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T15:31:38Z","timestamp":1774625498487,"version":"3.50.1"},"reference-count":33,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2010,11]]},"abstract":"<jats:p> Let G be a finite group. The prime graph \u0393(G) of G is defined as follows. The vertices of \u0393(G) are the primes dividing the order of G and two distinct vertices p, p\u2032 are joined by an edge if there is an element in G of order pp\u2032. In [G. Y. Chen et al., Recognition of the finite almost simple groups PGL<jats:sub>2<\/jats:sub>(q) by their spectrum, Journal of Group Theory, 10 (2007) 71\u201385], it is proved that PGL(2, p<jats:sup>k<\/jats:sup>), where p is an odd prime and k &gt; 1 is an integer, is recognizable by its spectrum. <\/jats:p><jats:p> It is proved that if p &gt; 19 is a prime number which is not a Mersenne or Fermat prime and \u0393(G) = \u0393(PGL(2, p)), then G has a unique nonabelian composition factor which is isomorphic to PSL(2, p). In this paper as the main result, we show that if p is an odd prime and k &gt; 1 is an odd integer, then PGL(2, p<jats:sup>k<\/jats:sup>) is uniquely determined by its prime graph and so these groups are characterizable by their prime graphs. <\/jats:p>","DOI":"10.1142\/s021819671000587x","type":"journal-article","created":{"date-parts":[[2010,11,12]],"date-time":"2010-11-12T04:22:08Z","timestamp":1289535728000},"page":"847-873","source":"Crossref","is-referenced-by-count":13,"title":["CHARACTERIZATION BY PRIME GRAPH OF PGL(2, p<sup>k<\/sup>) WHERE p AND k &gt; 1 ARE ODD"],"prefix":"10.1142","volume":"20","author":[{"given":"Z.","family":"AKHLAGHI","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Department of Pure Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"KHOSRAVI","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Department of Pure Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"KHATAMI","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Computer Science, Department of Pure Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424, Hafez Ave., Tehran 15914, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s10474-009-8048-7"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1112\/S0025579300007865"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/s10469-008-9003-3"},{"key":"rf4","first-page":"71","volume":"10","author":"Chen G. 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