On the Dirichlet polynomial of finite group of Lie type
Rendiconti del Seminario Matematico della Università di Padova, Tome 115 (2006), pp. 51-69. 
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     author = {Damian, Erika and Lucchini, Andrea},
     title = {On the {Dirichlet} polynomial of finite group of {Lie} type},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {51--69},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {115},
     year = {2006},
     mrnumber = {2245587},
     zbl = {1167.20334},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_2006__115__51_0/}
}
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Damian, Erika; Lucchini, Andrea. On the Dirichlet polynomial of finite group of Lie type. Rendiconti del Seminario Matematico della Università di Padova, Tome 115 (2006), pp. 51-69. http://www.numdam.org/item/RSMUP_2006__115__51_0/

[1] E. Artin, The orders of the classical simple groups. Comm. Pure Appl. Math., 8 (1955), pp. 455-472. | MR | Zbl

[2] D. M. Bloom, The subgroups of PSL(3; q) for odd q. Trans. Amer. Math. Soc., 127 (1967), pp. 150-178. | MR | Zbl

[3] K. S. Brown, The coset poset and probabilistic zeta function of a finite group. J. Algebra 225, 2 (2000), pp. 989-1012. | MR | Zbl

[4] R. W. Carter, Simple groups of Lie type. Wiley Classics Library. John Wiley & Sons Inc., New York, 1989. Reprint of the 1972 original, A WileyInterscience Publication. | MR | Zbl

[5] J. H. Conway - R. T. Curtis - S. P. Norton - R. A. Parker - R. A. Wilson, Atlas of finite groups. Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups, With computational assistance from J. G. Thackray. | MR | Zbl

[6] E. DAMIAN, - A. LUCCHINI, The Dirichlet polynomial of a finite group and the subgroups of prime power index. In Advances in group theory 2002. Aracne, Rome, 2003, pp. 209-221. | MR | Zbl

[7] E. Damian - A. Lucchini, Recognizing the alternating groups from their probabilistic zeta function. Glasgow Math. J., 46 (2004), pp. 595-599. | MR | Zbl

[8] E. DAMIAN, - A. LUCCHINI, The probabilistic zeta function of finite simple groups. J. Algebra, submitted. | MR | Zbl

[9] E. Damian - A. Lucchini - F. Morini, Some properties of the probabilistic zeta function on finite simple groups. Pacific J. Math., 215, 1 (2004), pp. 3-14. | MR | Zbl

[10] E. Detomi - A. Lucchini, Recognizing soluble groups from their probabilistic zeta functions. Bull. London Math. Soc., 35, 5 (2003), pp. 659-664. | MR | Zbl

[11] J. D. Dixon - B. Mortimer, Permutation groups, vol. 163 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1996. | MR | Zbl

[12] W. Feit, On large Zsigmondy primes. Proc. Amer. Math. Soc., 102, 1 (1988), pp. 29-36. | MR | Zbl

[13] R. Guralnick - T. Penttila - C. E. Praeger - J. Saxl, Linear groups with orders having certain large prime divisors. Proc. London Math. Soc. (3) 78, 1 (1999), pp. 167-214. | MR | Zbl

[14] P. Hall, The eulerian functions of a group. Quart. J. Math., 7 (1936), pp. 134-151. | JFM

[15] B. Huppert, Endliche Gruppen. I. Die Grundlehren der Mathematischen Wissenschaften, Band 134. Springer-Verlag, Berlin, 1967. | MR | Zbl

[16] W. Kimmerle - R. Lyons - R. Sandling - D. N. Teague, Composition factors from the group ring and Artin's theorem on orders of simple groups. Proc. London Math. Soc. (3) 60, 1 (1990), pp. 89-122. | MR | Zbl

[17] M. W. Liebeck - C. E. Praeger - J. Saxl, The maximal factorizations of the finite simple groups and their automorphism groups. Mem. Amer. Math. Soc., 86, (1990), p. 432. | MR | Zbl

[18] D. Quillen, Homotopy properties of the poset of nontrivial p-subgroups of a group. Adv. in Math., 28, 2 (1978), pp. 101-128. | MR | Zbl

[19] L. Solomon, The Steinberg character of a finite group with BN-pair. In Theory of Finite Groups (Symposium, Harvard Univ., Cambridge, Mass., 1968). Benjamin, New York, 1969, pp. 213-221. | MR | Zbl

[20] R. P. Stanley, Enumerative combinatorics. Vol. 1, vol. 49 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1997. | MR | Zbl

[21] M. Suzuki, A class of doubly transitive permutation groups. In Proc. Internat. Congr. Mathematicians (Stockholm, 1962). Inst. Mittag-Leffler, Djursholm, 1963, pp. 285-287. | MR | Zbl

[22] K. Zsigmondy, Zur Theorie der Potenzreste. Monatsh. Math. Phys., 3 (1892), pp. 265-284. | JFM | MR