On the Dirichlet polynomial of finite group of Lie type

Erika Damian; Andrea Lucchini

Rendiconti del Seminario Matematico della Università di Padova (2006)

  • Volume: 115, page 51-69
  • ISSN: 0041-8994

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Damian, Erika, and Lucchini, Andrea. "On the Dirichlet polynomial of finite group of Lie type." Rendiconti del Seminario Matematico della Università di Padova 115 (2006): 51-69. <http://eudml.org/doc/108685>.

@article{Damian2006,
author = {Damian, Erika, Lucchini, Andrea},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {finite simple groups; probabilistic zeta functions; irreducible Dirichlet polynomials; finite groups of Lie type},
language = {eng},
pages = {51-69},
publisher = {Seminario Matematico of the University of Padua},
title = {On the Dirichlet polynomial of finite group of Lie type},
url = {http://eudml.org/doc/108685},
volume = {115},
year = {2006},
}

TY - JOUR
AU - Damian, Erika
AU - Lucchini, Andrea
TI - On the Dirichlet polynomial of finite group of Lie type
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2006
PB - Seminario Matematico of the University of Padua
VL - 115
SP - 51
EP - 69
LA - eng
KW - finite simple groups; probabilistic zeta functions; irreducible Dirichlet polynomials; finite groups of Lie type
UR - http://eudml.org/doc/108685
ER -

References

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  1. [1] E. ARTIN, The orders of the classical simple groups. Comm. Pure Appl. Math., 8 (1955), pp. 455-472. Zbl0065.25703MR73601
  2. [2] D. M. BLOOM, The subgroups of PSL(3; q) for odd q. Trans. Amer. Math. Soc., 127 (1967), pp. 150-178. Zbl0153.03702MR214671
  3. [3] K. S. BROWN, The coset poset and probabilistic zeta function of a finite group. J. Algebra 225, 2 (2000), pp. 989-1012. Zbl0973.20016MR1741574
  4. [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. Zbl0723.20006MR1013112
  5. [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. Zbl0568.20001MR827219
  6. [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. Zbl1070.20025MR2053446
  7. [7] E. DAMIAN - A. LUCCHINI, Recognizing the alternating groups from their probabilistic zeta function. Glasgow Math. J., 46 (2004), pp. 595-599. Zbl1071.20060MR2094813
  8. [8] E. DAMIAN, - A. LUCCHINI, The probabilistic zeta function of finite simple groups. J. Algebra, submitted. Zbl1127.20052MR2329578
  9. [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. Zbl1113.20063MR2060491
  10. [10] E. DETOMI - A. LUCCHINI, Recognizing soluble groups from their probabilistic zeta functions. Bull. London Math. Soc., 35, 5 (2003), pp. 659-664. Zbl1045.20054MR1989495
  11. [11] J. D. DIXON - B. MORTIMER, Permutation groups, vol. 163 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1996. Zbl0951.20001MR1409812
  12. [12] W. FEIT, On large Zsigmondy primes. Proc. Amer. Math. Soc., 102, 1 (1988), pp. 29-36. Zbl0639.10007MR915710
  13. [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. Zbl1041.20035MR1658168
  14. [14] P. HALL, The eulerian functions of a group. Quart. J. Math., 7 (1936), pp. 134-151. Zbl0014.10402JFM62.0082.02
  15. [15] B. HUPPERT, Endliche Gruppen. I. Die Grundlehren der Mathematischen Wissenschaften, Band 134. Springer-Verlag, Berlin, 1967. Zbl0217.07201MR224703
  16. [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. Zbl0668.20009MR1023806
  17. [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. Zbl0703.20021MR1016353
  18. [18] D. QUILLEN, Homotopy properties of the poset of nontrivial p-subgroups of a group. Adv. in Math., 28, 2 (1978), pp. 101-128. Zbl0388.55007MR493916
  19. [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. Zbl0216.08001MR246951
  20. [20] R. P. STANLEY, Enumerative combinatorics. Vol. 1, vol. 49 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1997. Zbl0889.05001MR1442260
  21. [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. Zbl0116.25801MR175966
  22. [22] K. ZSIGMONDY, Zur Theorie der Potenzreste. Monatsh. Math. Phys., 3 (1892), pp. 265-284. MR1546236JFM24.0176.02

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