[1]

E. A. Bertram, “Some Applications of Graph Theory to Finite Groups,” Discrete Mathematics, Vol. 44, No. 1, 1983, pp. 3143. doi:10.1016/0012365X(83)900043

[2]

B. Bollobas, “Graph Theory,” Springer, Berlin, 1979.
doi:10.1007/9781461299677

[3]

Y. Segev, “The Commuting Graph of Minimal NonSolvable Groups,” Geometriae Dedicata, Vol. 88, No. 13, 2001, pp. 5566.

[4]

C. T. Marchionna, “Distance in a Group and ErdosType Graph,” Istituto Lombardo Accademia di Scienze e Lettere (Classe di Scienze Matematiche e Naturali), Vol. 125, 1992, pp. 323.

[5]

E. A. Bertram, M. Herzog and A. Mann, “On a Graph Related to Conjugacy Classes of Groups,” Bulletin of the London Mathematical Society, Vol. 22, No. 6, 1990, pp. 569575.
doi:10.1112/blms/22.6.569

[6]

M. Bianchi, D. Chillag, A. G. B. Mauri, M. Herzog, M. and C. Scoppola, “Applications of a Graph Related to Conjugacy Classes in Finite Groups,” Archiv der Mathematik, Vol. 58, 1992, pp. 126132.
doi:10.1007/BF01191876

[7]

D. Chillag, M. Herzog and A. Mann, “On the Diameter of a Graph Related to Conjugacy Classes of Groups,” Bulletin of the London Mathematical Society, Vol. 25, No. 3, 1993, pp. 255262. doi:10.1112/blms/25.3.255

[8]

M. Herzog, P. Longobardi and M. Maj, “On a Commuting Graph on Conjugacy Classes of Groups,” Communications in Algebra, Vol. 37, No. 10, 2009, pp. 33693387.

[9]

A. Abdollahi, S. Akbari and H. R. Maimani, “NonCommuting Graph of a Group,” Journal of Algebra, Vol. 298, No. 2, 2006, pp. 468492.
doi:10.1016/j.jalgebra.2006.02.015

[10]

S. Akbari and A. Mohammadian, “On the ZeroDivisor Graph of a Commutative Ring,” Journal of Algebra, Vol. 274, No. 2, 2004, pp. 847855.

[11]

S. Akbari, A. Mohammadian, H. Radjavi and P. Raja, “On the Diameters of Commuting Graphs,” Linear Algebra and Its Applications, Vol. 418, No. 1, 2006, pp. 161176.

[12]

S. Akbari, H. Bidkhori and A. Mohammadian, “Commuting Graphs of Matrix Algebras,” Communications in Algebra, Vol. 36, No. 11, 2008, pp. 40204031.

[13]

M. Akbari, M. Kheirabadi and A. R. Moghaddamfar, “Recognition by NonCommuting Graph of Finite Simple Groups L4(q),” Frontiers of Mathematics in China, Vol. 6, No. 1, 2011, pp. 116. doi:10.1007/s1146401000856

[14]

N. Ahanjideh and A. Iranmanesh, “A Characterization of Bn(q) by the Set of Orders of Maximal Abelian Subgroups,” International Journal of Algebra and Computation, Vol. 19, No. 2, 2009, pp. 191211.
doi:10.1142/S0218196709005020

[15]

N. Ahanjideh and A. Iranmanesh, “On the Relation between the NonCommuting Graph and the Prime Graph,” International Journal of Group Theory, Vol. 1, No. 1, 2012, pp. 2528.

[16]

G. Y. Chen, “A Characterization of Alternating Groups by the Set of Orders of Their Maximal Abelian Subgroups,” Siberian Mathematical Journal, Vol. 47, No. 3, 2006, pp. 594596. doi:10.1007/s1120200600701

[17]

M. R. Darafsheh, “Groups with the Same NonCommuting Graph,” Discrete Applied Mathematics, Vol. 157, No. 4, 2009, pp. 833837. doi:10.1016/j.dam.2008.06.010

[18]

M. R. Darafsheh and A. D. Monfared, “A Characterization of the Groups PSU(4,4) and PSL(4,4) by NonCommuting Graph,” Utilitas Mathematica, Vol. 81, 2010, pp. 165185.

[19]

M. Kheirabadi and A. R. Moghaddamfar, “Recognizing Some Finite Simple Groups by NonCommuting Graph,” Journal of Algebra and Its Applications, Vol. 11, No. 4, 2012, 14 pages. doi:10.1142/S0219498812500776

[20]

M. C. Xu, “The Characterization of Finite Simple Groups, L_{3}(3^{2m1}) (m ≥ 2) by Their Element Orders,” Acta Mathematica Sinica, Vol. 21, No. 4, 2005, pp. 899902.
doi:10.1007/s1011400404486

[21]

A. Erfanian and B. Tolue, “Relative NonCommuting Graph of a Finite Group,” Journal of Algebra and Its Applications, in press. doi:10.1142/S0219498812501575

[22]

A. Erfanian and F. G. Russo, “Probability of Commuting nTuples in Some Classes of Compact Groups,” Bulletin of the Iranian Mathematical Society, Vol. 24, 2008, pp. 2737.

[23]

K. H. Hofmann and F. G. Russo, “The Probability That x and y Commute in a Compact Group,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 153, 2012, pp. 557571.

[24]

P. Niroomand, R. Rezaei and F. G. Russo, “Commuting Prowers and Exterior Degree of Finite Groups,” Journal of the Korean Mathematical Society, Vol. 49, No. 4, 2012, pp. 855865. doi:10.4134/JKMS.2012.49.4.855

[25]

R. Rezaei and F. G. Russo, “nth Relative Nilpotency Degree and Relative nIsoclinism Classes,” Carpathian Journal of Mathematics, Vol. 27, No. 1, 2011, pp. 123130.

[26]

S. Dolfi, E. Pacifici, L. Sanus and P. Spiga, “On the Vanishing Prime Graph of Finite Groups,” Journal of the London Mathematical Society, Vol. 82, No. 1, 2010, pp. 167183.

[27]

S. Dolfi, E. Pacifici, L. Sanus and P. Spiga, “On the Vanishing Prime Graph of Solvable Groups,” Journal of Group Theory, Vol. 13, No. 2, 2010, pp. 189206.
doi:10.1515/jgt.2009.046

[28]

K. W. Gruenberg and O. Kegel, Manuscript, unpublished, 1975.

[29]

N. Iiyori and H. Yamaki, “Prime Graph Components of the Simple Groups of Lie Type over the Field of Even Characteristic,” Journal of Algebra, Vol. 155, No. 2, 1993, pp. 335343. doi:10.1006/jabr.1993.1048

[30]

A. Kondratev, “Prime Graph Components of Finite Simple Groups,” Mathematics of the USSRSbornik, Vol. 67, No. 1, 1990, pp. 235247.
doi:10.1070/SM1990v067n01ABEH001363

[31]

A. Kondratev and V. D. Mazurov, “Recognition of Alternating Groups of Prime Degree from the Orders of Their Elements,” Siberian Mathematical Journal, Vol. 41, No. 2, 2000, pp. 294302. doi:10.1007/BF02674599

[32]

M. S. Lucido, “The Diameter of the Prime Graph of Finite Groups,” Journal of Group Theory, Vol. 2, No. 2, 1999, pp. 157172. doi:10.1515/jgth.1999.011

[33]

M. S. Lucido, “Prime Graph Components of Finite Almost Simple Groups,” Rendiconti del Seminario Matematico della Università di Padova, Vol. 102, 1999, pp. 122.

[34]

M. S. Lucido and A. R. Moghaddamfar, “Groups in Which All the Connected Components of Their Prime Graphs are Complete,” Journal of Group Theory, Vol. 7, No. 3, 2004, pp. 373384. doi:10.1515/jgth.2004.013

[35]

A .V. Vasilev, “On a Relation between the Structure of a Finite Group and the Properties of Its Prime Graph,” Siberian Mathematical Journal, Vol. 46, No. 3, 2005, pp. 396404. doi:10.1007/s112020050042x

[36]

A. V. Vasilev and E. P. Vdovin, “An Adjacency Criterion in the Prime Graph of a Finite Simple Group,” Algebra Logic, Vol. 44, No. 6, 2005, pp. 381406.
doi:10.1007/s1046900500375

[37]

J. S. Williams, “Prime Graph Components of Finite Groups,” Journal of Algebra, Vol. 69, No. 2, 1981, pp. 487513.
doi:10.1016/00218693(81)902180

[38]

Z. Akhlaghi, B. Khosravi and M. Khatami, “Quasirecognition by Prime Graph of Simple Group Dn(3),” Publicationes Mathematicae Debrecen, Vol. 78, 2011, pp. 469 484. doi:10.5486/PMD.2011.4851

[39]

Z. Arad and W. Herfort, “Maximal Cyclic Subgroups and Prime Divisors in Finite Groups,” Archiv der Mathematik, Vol. 85, No. 1, 2005, pp. 3136.
doi:10.1007/s0001300514496

[40]

M. R. Darafsheh, A. R. Moghaddamfar and A. R. Zokayi, “A Characterization of Finite Simple Groups by the Degrees of Vertices of Their Prime Graphs,” Algebra Col loquium, Vol. 12, 2005, pp. 431442.

[41]

H. He and W. Shi, “Recognition of Some Finite Simple Groups of Type D_{n}(q) by Spectrum,” International Journal of Algebra and Computation, Vol. 19, No. 1, 2009, pp. 681698.

[42]

A. Khosravi and B. Khosravi, “2Recognizability of PSL(2,p2) by the Prime Graph,” Siberian Mathematical Journal, Vol. 49, No. 4, 2008, pp. 749757.
doi:10.1007/s1120200800722

[43]

A. Khosravi and B. Khosravi, “Quasirecognition of the Simple Group 2G2(q) by the Prime Graph,” Siberian Mathematical Journal, Vol. 48, No. 3, 2007, pp. 570577.

[44]

B. Khosravi, B. Khosravi and B. Khosravi, “On the Prime Graph of PSL(2,p) Where p>3 Is a Prime Number,” Acta Mathematica Hungarica, Vol. 116, No. 4, 2007, pp. 295307. doi:10.1007/s104740076021x

[45]

A. Khosravi and B. Khosravi, “A New Characterization of Almost Sporadic Groups,” Journal of Algebra and Its Applications, Vol. 1, No. 3, 2002, pp. 267279.
doi:10.1142/S021949880200015X

[46]

A. Iranmanesh and A. Jafarzadeh, “On the Commuting Graph Associated with the Symmetric and Alternating Groups,” Journal of Algebra and Its Applications, Vol. 7, No. 4, 2008, pp. 129146.
doi:10.1142/S0219498808002710

[47]

V. D. Mazurov and A. R. Moghaddamfar, “The Recognition of the Simple Group S_{8}(2) by Its Spectrum,” Algebra Colloquium, Vol. 13, No. 4, 2006, pp. 643646.

[48]

J. Conway, R. Curtis, S. Norton, R. Parker and R. Wilson, “Atlas of Finite Groups,” Clarendon Press, Oxford, 1985.

[49]

E. I. Khukhro and V. D. Mazurov, “Unsolved Problems in Group Theory: The Kourovka Notebook,” 17th Edition, Sobolev Institute of Mathematics, Novosibirsk, 2010.

[50]

A. Arikan and U. Meierfrankenfeld, “Hypersolvable Groups,” Communications in Algebra, Vol. 34, No. 10, 2006, pp. 36433657. doi:10.1080/00927870600860742

[51]

M. D. Dixon, “Sylow Theory, Formations and Fitting Classes in Locally Finite Groups,” World Scientific Publishing Corporation, River Edge, 1994.

[52]

O. H. Kegel and B. A. F. Wehrfritz, “Locally Finite Groups,” North Holland, Amsterdam, 1973.

[53]

F. G. Russo, “Generalized FCGroups in Finitary Groups,” University of Naples Federico II, 2007.
http://www.fedoa.unina.it/1305

[54]

A. D’Aniello, C. De Vivo and G. Giordano, “Lattice For mations and Sylow Normalizers: A Conjecture,” Atti del Seminario Matematico e Fisico dell’Universita’ di Modena e Reggio Emilia, Vol. 55, 2007, pp. 107112.

[55]

L. Kazarin, A. MartinezPastor and M. D. PerezRamos, “On the Sylow Graph of a Group and Sylow Normalizers,” Israel Journal of Mathematics, Vol. 186, No. 1, 2011, pp. 251271. doi:10.1007/s118560110138x

[56]

F. G. Russo, “On the Connectivity of the Sylow Graph of a Finite Group,” Cornell University Library, 2010.
http://arxiv.org/abs/1002.4853.

[57]

A. D’Aniello, C. De Vivo and G. Giordano, “Finite Groups with Primitive Sylow Normalizers,” Bollettino dell’Unione Matematica Italiana (Sezione B), Vol. 5, 2002, pp. 235245.

[58]

A. D’Aniello, C. De Vivo and G. Giordano, “Saturated Formations and Sylow Normalisers”, Bulletin of the Australian Mathematical Society, Vol. 69, No. 1, 2004, pp. 2533.

[59]

A. D’Aniello, C. De Vivo, G. Giordano and M. D. PerezRamos, “Saturated Formations Closed under Sylow Normalizers,” Communications in Algebra, Vol. 33, 2005, pp. 28012808. doi:10.1081/AGB200065377

[60]

A. D’Aniello, C. De Vivo and G. Giordano, “On Certain Saturated Formations of Finite Groups,” Proceedings of Ischia Group Theory 2006, Singapore, 2008, pp. 1231.

[61]

K. Doerk and T. Hawkes, “Finite Soluble Groups, de Gruyter, Berlin, 1992.

[62]

G. Glauberman, “PrimePower Factor Groups of Finite Groups,” Mathematische Zeitschrift, Vol. 107, No. 3, 1968, pp. 159172. doi:10.1007/BF01110255

[63]

G. Glauberman, “PrimePower Factor Groups of Finite Groups II,” Mathematische Zeitschrift, Vol. 117, No. 14, 1970, pp. 4656. doi:10.1007/BF01109827

[64]

A. BallesterBolinches and L. A. Shemetkov, “On Normalizers of Sylow Subgroups in Finite Groups,” Siberian Mathematical Journal, Vol. 40, No. 1, 1999, pp. 35.

[65]

A. BallesterBolinches, A. MartinezPastor, M. C. PedrazaAguilera and M.D. PerezRamos, “On NilpotentLike Fitting Formations,” Cambridge University Press, Cambdridge, 2003, pp. 3138.

[66]

A. BallesterBolinches, L. M. Ezquerro and A. N. Skiba, “Local Embeddings of Some Families of Subgroups of Finite Groups,” Acta Mathematica Sinica, Vol. 25, No. 6, 2009, pp. 869882. doi:10.1007/s1011400986234

[67]

A. BallesterBolinches and L. M. Ezquerro, “Classes of Finite Groups,” Springer, Heidelberg, 2006.

[68]

B. Baumann and U. Meierfrankenfeld, “On Normalizers of Nilpotent Subgroups,” Journal of Algebra, Vol. 268, No. 2, 2003, pp. 373403.
doi:10.1016/S00218693(03)000942

[69]

M. Bianchi, A. G. B. Mauri and P. Hauck, “On Finite Groups with Nilpotent SylowNormalizers,” Archiv der Mathematik, Vol. 47, 1986, pp. 93197.

[70]

R. Bryce, V. Fedri and L. Serena, “Bounds on the Fitting Length of Finite Solvable Groups with Supersoluble Sylow Normalisers,” Bulletin of the Australian Mathematical Society, Vol. 44, No. 1, 1991, pp. 1931.
doi:10.1017/S0004972700029427

[71]

B. Sirola, “Normalizers and SelfNormalizing Subgroups II,” Central European Journal of Mathematics, Vol. 9, No. 6, 2011, pp. 13171332.
doi:10.2478/s1153301100912

[72]

B. Sirola, “On Centralizers and Normalizers for Groups,” Bulletin of the Australian Mathematical Society, 2012, in press.

[73]

The GAP Group, “GAP: Groups, Algorithms and Programming,” Version 4.4, 2005.
http://www.gapsystem.org.
