The Chebotarev Invariant of a Finite Group

REFERENCES

• Arratia , [Arratia et al. 03] R. , Barbour , A. D. and Tavaré , S. 2003 . Logarithmic Combinatorial Structures: A Probabilistic Approach, E.M.S. Monographs , Zurich : European Mathematical Society .
   Google Scholar
• Arratia , [Arratia and Tavaré 92] R. and Tavaré , S. 1992 . “The Cycle Structure of Random Permutations.” . Annals of Prob. , 20 : 1567 – 1591 .
   Web of Science ®Google Scholar
• Bosma , [Bosma et al. 97] W. , Cannon , J. and Playoust , C. 1997 . “The Magma Algebra System, I. The User Language.” . J. Symbolic Comput. , 24 : 235 – 265 . See also http://magma.maths.usyd.edu.au/magma/
   Web of Science ®Google Scholar
• Dixon , [Dixon 92] J. D. 1992 . “Random Sets Which Invariably Generate the Symmetric Group.” . Discrete Math. , 105 : 25 – 39 .
   Web of Science ®Google Scholar
• Dixon , [Dixon 02] J. D. 2002 . “Probabilistic Group Theory.” . C.R. Math. Rep. Acad. Sci. Canada , 24 : 1 – 15 .
   Google Scholar
• Flajolet , [Flajolet et al. 92] P. , Gardy , D. and Thimonier , L. 1992 . “Birthday Paradox, Coupon Collectors, Caching Algorithms and Self-Organizing Search.” . Discrete Applied Math. , 39 : 207 – 229 .
   Web of Science ®Google Scholar
• Fulman , [Fulman and Guralnick 03] J. and Guralnick , R. 2003 . “Derangements in Simple and Primitive Groups.” . In Groups, Combinatorics, and Geometry (Durham, 2001) , 99 – 121 . River Edge , NJ : World Sci. Publ. .
   Google Scholar
• Fulton , [Fulton and Harris 91] W. and Harris , J. 1991 . Representation Theory. A First Course, Grad. Texts in Math. 129. , New York : Springer .
   Google Scholar
• Gallagher , [Gallagher 73] P. X. 1973 . “The Large Sieve and Probabilistic Galois Theory.” . In Proc. Sympos. Pure Math. , Vol. XXIV , 91 – 101 . Providence : Amer. Math. Soc. .
   Google Scholar
• Goncharov , [Goncharov 44] V. 1944 . “Du domaine d’analyse combinatoire.” . Bull. Acad. Sci. USSR Ser. Mat. (Izv. Akad. Nauk SSSR) , 8 : 3 – 48 . Amer. Math. Soc. Transl. (2) 19 (1962), 1–46.
   Google Scholar
• Jouve , [Jouve et al. 08] F. , Kowalski , E. and Zywina , D. 2008 . “An Explicit Integral Polynomial Whose Splitting Field Has Galois Group W(E 8).” . Journal de Théorie des Nombres de Bordeaux , 20 : 761 – 782 .
   Google Scholar
• Jouve , [Jouve et al. 10] F. , Kowalski , E. and Zywina , D. 2010 . “Splitting Fields of Characteristic Polynomials of Random Elements in Arithmetic Groups.” . arXiv , : 1008.3662
   Google Scholar
• Kantor , [Kantor and Lubotzky 90] W. M. and Lubotzky , A. 1990 . “The Probability of Generating a Finite Classical Group.” . Geom. Dedicata , 36 : 67 – 87 .
   Web of Science ®Google Scholar
• Kantor , [Kantor et al. 10] W. M. , Lubotzky , A. and Shalev , A. 2010 . “Invariable Generation and the Chebotarev Invariant of a Finite Group.” . arXiv , : 1010.5722
   Google Scholar
• Kowalski , [Kowalski and Zywina 11] E. and Zywina , D. 2011 . “The Chebotarev Invariant of a Finite Group.” . arXiv , : 1008.4909
   Google Scholar
• Lagarias , [Lagarias et al. 79] J. C. , Montgomery , H. L. and Odlyzko , A. M. 1979 . “A Bound for the Least Prime Ideal in the Chebotarev Density Theorem.” . Inventiones math. , 54 : 271 – 296 .
   Web of Science ®Google Scholar
• Lloyd , [Lloyd and Shepp 66] S. P. and Shepp , L. A. 1966 . “Ordered Cycle Lengths in a Random Permutation.” . Trans. Amer. Math. Soc. , 121 : 340 – 357 .
   Web of Science ®Google Scholar
• Łuczak , [Łuczak and Pyber 93] T. and Pyber , L. 1993 . “On Random Generation of the Symmetric Group.” . Combin. Probab. Comput. , 2 : 505 – 512 .
   Google Scholar
• Pomerance , [Pomerance 01] C. 2001 . “The Expected Number of Random Elements to Generate a Finite Abelian Group.” . Period. Math. Hungar. , 43 : 191 – 198 .
   Google Scholar
• Rose , [Rose 94] J. S. 1994 . A Course on Group Theory , New York : Dover .
   Google Scholar
• Serre , [Serre 72] J.-P. 1972 . “Propriétés galoisiennes des points d’ordre fini des courbes elliptiques.” . Invent. math. , 15 : 259 – 331 .
   Google Scholar
• Serre , [Serre 98] J.-P. 1998 . Abelian ℓ-adic Representations and Elliptic Curves, Res. Notes Math , Wellesley : A. K. Peters .
   Google Scholar
• Serre , [Serre 02] J.-P. 2002 . “On a Theorem of Jordan.” . Math. Medley , 29 : 3 – 18 . also in Bull. AMS 40 (2003), 429–440.
   Google Scholar