Return to my main page.

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 (2003), 5485-5503.
  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, Algeba 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. 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.
  44. Lewis, Mark L., Nuclei and lifts of pi-partial characters, to appear in Algebra Coll.
  45. Aziziheris, Kamal and Lewis, Mark L., Counting the number of nonlinear irreducible characters of a finite group, to appear in Comm. Algebra.
  46. Lewis, Mark L., Generalizing Camina groups and their character tables, to appear in J. Group Theory.
  47. Lewis, Mark L., Character Tables of groups where all nonlinear characters vanish off the center, to appear in the proceedings of Ischia group theory conference 2008.
  48. Lewis, Mark L. and McVey, John K., Character degree graphs of automorphism groups of characteristically simple groups, to appear in J. Group Theory.
  49. Lewis, Mark L., The vanishing-off subgroup, submitted.
  50. Lewis, Mark L., Brauer pairs of Camina p-groups of nilpotence class 2, submitted.
  51. Lewis, Mark L., A group with three real irreducible characters: answering a question of Moreto and Navarro, 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.
  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.

A character table

  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.

Return to my main page.