Mark L. Lewis

Mark Lewis

 

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Research Publications for Mark L. Lewis

  1. Lewis, Mark L., Solvable groups having almost relatively prime irreducible character degrees, J. Algebra, 174 (1995), 197-216.
  2. Lewis, Mark L., Characters of maximal subgroups of M-groups, J. Algebra, 183 (1996), 864-897.
  3. Lewis, Mark L., Nonabelian fully-ramified sections, Can. J. Math., 48 (1996), 997-1017.
  4. Lewis, Mark L., A family of groups containing a nonabelian fully-ramified section, J. Algebra, 186 (1996), 578-596.
  5. Lewis, Mark L., Primitive characters of subgroups of M-groups, Proc. AMS, 125 (1997), 27-33.
  6. Lewis, Mark L., Character correspondences and nilpotent fully-ramified sections, Comm. Algebra, 25 (1997), 3587-3604.
  7. Lewis, Mark L., Characters, coprime actions, and operator groups, Archiv. der Math, 69 (1997), 455-460.
  8. Lewis, Mark L., Derived Lengths and character degrees , Proc. AMS, 126 (1998), 1915-1921.
  9. Lewis, Mark L., Derived lengths of solvable groups satisfying the one-prime hypothesis, Comm. Algebra, 26 (1998), 2419-2428.
  10. Lewis, Mark L., Determining group structure from sets of irreducible character degrees, J. Algebra, 206 (1998), 235-260.
  11. Lewis, Mark L., Irreducible character degree sets of solvable groups, J. Algebra, 206 (1998), 208-234.
  12. Gagola, Stephen, Jr. and Lewis, Mark L., Squares of character that are the sum of all irreducible characters, Ill. J. Math, 42 (1998), 655-672.
  13. Gagola, Stephen, Jr. and Lewis, Mark L., A character theoretic condition characterizing nilpotent groups, Comm. Algebra, 27 (1999), 1053-1056.
  14. Isaacs, I. M.; Lewis, Mark L.; and Navarro, Gabriel, Invariant characters and coprime actions on finite nilpotent groups, Archiv. der Math., 74 (2000), 401-409.
  15. Lewis, Mark L., Fitting heights and the character degree graph, Archiv. der Math., 75 (2000), 338-341.
  16. Lewis, Mark L., Inducing characters of prime power degree, Osaka J. Math., 37 (2000), 735-744.
  17. Lewis, Mark L., Solvable groups whose degree graphs have two connected components, J. Group Theory, 4 (2001), 255-275.
  18. Isaacs, I. M., and Lewis, Mark L., Derived lengths of solvable groups satisfying the one-prime hypothesis II, Comm. Algebra, 29 (2001), 2285-2292.
  19. Lewis, Mark L., Bounding Fitting heights of character degree graphs, J. Algebra, 242 (2001), 810-818.
  20. Lewis, Mark L., Derived lengths of solvable groups having five irreducible character degrees I, Algebras and Representation Theory, 4 (2001), 469-489.
  21. Lewis, Mark L. and Riedl, Jeffrey M., Affine Semi-linear groups with three irreducible character degrees, J. Algebra, 264 (2001), 708-720.
  22. Lewis, Mark L., Derived lengths of solvable groups satisfying the one-prime hypothesis III, Comm. Algebra, 29 (2001), 5755-5767.
  23. Lewis, Mark L., A solvable group whose character degree graph has diameter 3, Proc. AMS , 130 (2002), 625-630.
  24. Lewis, Mark L., Derived lengths of solvable groups having five irreducible character degrees II, Algebras and Representation Theory, 5 (2002), 277-304.
  25. Lewis, Mark L., Solvable groups with degree graphs having 5 vertices and diameter 3, Comm. Algebra, 30 (2002), 5485-5503. At EBSCO
  26. Lewis, Mark L. and White, Donald L., Connectedness of degree graphs of nonsolvable groups, J. Algebra, 266 (2003), 51-76.
  27. Lewis, Mark L.; McVey, John K.; Moreto, Alexander; and Sanus, Lucia, A graph associated with the pi-character degrees of a group, Archiv. der Math, 80 (2003), 570-577.
  28. Isaacs, I. M. and Lewis, Mark L., Inductive sources and subnormal subgroups, Archiv. der Math., 83 (2004), 204-207.
  29. Lewis, Mark L. and White, Donald L., Diameters of degree graphs of nonsolvable groups, Journal of Algebra , 283 (2005), 80-92.
  30. Lewis, Mark L., Classifying character degree graphs with five vertices. In: Finite Groups 2003. Edited by C. Y. Ho, P. Sin, P. H. Tiep, and A. Turull. de Gruyter, Berlin, 2004, 247-265.
  31. Lewis, Mark L., Moreto, Alexander, and Wolf, Thomas R., Non-divisibility among character degrees, Journal of Group Theory, 8 (2005), 561-588.
  32. Lewis, Mark L., Disconnectedness and diameters of degree graphs associated with normal subgroups, Comm. Algebra , 33 (2005), 3419-3437.
  33. Lewis, Mark L., The number of irreducible character degrees of solvable groups satisfying the one-prime hypothesis, Algebras and Representation Theory, 8 (2005), 479-497.
  34. Lewis, Mark L., Character degree graphs of solvable groups of Fitting height 2, Bull. Can. Math. Soc., 49 (2006), 127-133.
  35. Lewis, Mark L., Obtaining nuclei from chains of normal subgroups, J. Algebra Appl., 5 (2006), 215-229.
  36. Isaacs, I. M.; Keller, Thomas Michael; Lewis, Mark L.; and Moreto, Alexander, Transitive permutation groups all of whose derangements are involutions, J. Pure Appl. Algebra, 207 (2006), 717-724.
  37. Lewis, Mark L., Induction and restriction of lifts of pi-partial characters, Algebra Coll., 13 (2006), 607-616.
  38. Bianchi, Mariagrazi; Chillag, David; Lewis, Mark L.; and Pacifici, Emanuele, Character degree graphs that are complete graphs, Proc. AMS, 135 (2007), 671-676.
  39. Lewis, Mark L. and White, Donald L., Diameters of degree graphs of nonsolvable groups II, J. Algebra , 312 (2007), 634-649.
  40. Lewis, Mark L. and White, Donald L., Nonsolvable groups satisfying the one-prime hypothesis, Algebras and Representation Theory, 10 (2007), 379-412.
  41. Lewis, Mark L., Generalizing of a theorem of Huppert and Manz, J. Algebra Appl., 6 (2007), 687-695.
    42. At EBSCO

    Here is a page that contains all the information I obtained from MAGMA for this paper, and the code I used to find it.

  42. Cossey, James P. and Lewis, Mark L., Fong characters and chains of normal subgroups, Archiv. der Math., 89 (2007), 193-201.
  43. Lewis, Mark L., Subnormal inductive sources and pi-partial characters, Algebra Coll., 15 (2008), 405-413.  At EBSCO
  44. Lewis, Mark L., Nuclei and lifts of pi-partial characters, Algebra Coll., 16 (2009), 167-180. At EBSCO
  45. Lewis, Mark L., The vanishing-off subgroup, J. Algebra 321 (2009), 1313-1325.

    46. Here is a page with code for MAGMA that I wrote to compute the vanishing off subgroup of a group.

  46. Lewis, Mark L., Brauer pairs of Camina p-groups of nilpotence class 2, Archiv. der Math. 92 (2009), 95-98.
  47. Lewis, Mark L., Generalizing Camina groups and their character tables, J. Group Theory 12 (2009), 209-218.  At EBSCO
  48. Aziziheris, Kamal and Lewis, Mark L., Counting the number of nonlinear irreducible characters of a finite group, Comm. Algebra 37 (2009), 1572-1578.
  49. Lewis, Mark L. and McVey, John K., Character degree graphs of automorphism groups of characteristically simple groups, J. Group Theory 12 (2009), 387-391.  At EBSCO
  50. Lewis, Mark L., A group with three real irreducible characters: answering a question of Moreto and Navarro, J. Algebra Appl. 8 (2009), 453-459.
    51.   At EBSCO

      Here is the character table for the group I found with three real irreducible characters. This character table was computed by the computer system MAGMA. The character table is also available as an rtf-file and as a pdf-file. If you would like this in some other format, let me know, and I will see if I can get it into that format. Here is the file for inputing this group into MAGMA as polycyclic group as an html-file and as an txt-file.

  51. Lewis, Mark L., Character tables of groups where all nonlinear characters vanish off the center, Ischia group theory 2008, Edited by M. Bianchi, P. Longobardi, M. Maj, and C. M. Scoppola, World Scientific, New Jersey, 2009, 174-182.
  52. Lewis, Mark L., Groups where all the irreducible characters are super-monomial, Proc. AMS 138 (2010), 9-16.
  53. Lewis, Mark L., Lifts of partial characters with respect to a chain of normal subgroups, Algebr. Represent. Theory 13 (2010), 661-672.
  54. Cossey, James P. and Lewis, Mark L., Lifts of partial characters with cyclic defect groups, J. of Australian Math Society 89 (2010), 145-163.
  55. Cossey, James P., Lewis, Mark L., and Gabriel Navarro, The number of lifts of a Brauer character with a normal vertex, J. Algebra 328 (2011), 484-487.
  56. Lewis, Mark L. and White, Donald L., Nonsolvable groups all of whose character degrees are odd-square-free, Comm. Algebra 39 (2011), 1273-1292.
  57. Imperatore, Diana and Lewis, Mark L., A condition in finite solvable groups related to cyclic subgroups, Bull. Aust. Math. Soc. 83 (2011), 267-272.
  58. Cossey, James P. and Lewis, Mark L., Inductive pairs and lifts in solvable groups, J. Group Theory 14 (2011), 201-212.  AT EBSCO
  59. Lewis, Mark L. and White, Donald L., Nonsolvable groups for which no prime divides three character degrees, J. Algebra 336 (2011), 158-183.
  60. Lewis, Mark L., Inducing pi-partial characters with a given vertex, to appear in Ischia Group Theory 2010.  Preprint.
  61. Lewis, Mark L. and Meng, Qingyun, Square character degree graphs yield direct products, J. Algebra 49 (2012), 185-200.
  62. Cossey, James P. and Lewis, Mark L., Lifts and vertex pairs in solvable groups, Proc. Edinburgh Math. Soc 55 (2012), 143-153.  Preprint.
  63. Hamblin, James and Lewis, Mark L., Solvable groups satisfying the two-prime hypothesis II, to appear in Algebr. Represent. Theory.
  64. Lewis, Mark L. and Wilson, James B.,  Isomorphism in expanding families of indistinguishable groups, to appear Groups. Complexity. Cryptology.  Preprint.
  65. Lewis, Mark L., Bounding an index by the largest character degree of a solvable group, submitted.  Preprint.
  66. Cossey, James P. and Lewis, Mark L., Counting characters in blocks of solvable groups with abelian defect group, submitted.  Preprint.
  67. Lewis, Mark L., p-group Camina pairs, submitted.  Preprint.

Expository Publications for Mark L. Lewis (Refereed)

  1. Lewis, Mark L. and White, Donald L., Corrigendum for "Connectedness of degree graphs of nonsolvable groups" [J. Algebra, 266 (2003) 51-76], J. Algebra, 290 (2005), 594-598.
  2. Lewis, Mark L., M-groups of order p^aq^b: A theorem of Loukaki, J. Algebra Appl., 5 (2006), 465-503.  At EBSCO
  3. Lewis, Mark L., An overview of graphs associated with character degrees and conjugacy class sizes in finite groups, Rocky Mountain J. Math, 38 (2008), 175-211.
  4. Lewis, Mark L., Corrigendum to ''Determining group structure from sets of irreducible character degrees" [J.Algebra 206 (1998) 235-260], J. Algebra 322 (2009), 2251-2252.
  5. Lewis, Mark L., Classifying Camina groups: a theorem of Dark and Scoppola, submitted.

Preprint

  1. Cossey, James P. and Lewis, Mark L., Counting lifts of Brauer characters. Deposited at: <arXiv:1007.3011>.

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