Thomas Michael Keller Professor of Mathematics Office: Math/CS 557 Phone: 512-245-3735 Fax: 512-245-3425 Email: tk04@txstate.edu Home Page

Research Interests: Group Theory

Dr. Keller received his Ph.D. from the University of Mainz in 1995. Dr. Keller's recent research has been in the (classical) representation theory of finite groups and has dealt with the longstanding problem of finding a good bound for the derived length of a finite solvable group in terms of the number of its irreducible complex character degrees. This work is based on a study of the orbit sizes that are induced by the action of linear groups on finite vector spaces and involves many combinatorial questions as well as problems on permutation groups which are of independent interest.

Selected Publications

• Isaacs, I. M.; Keller, Thomas Michael; Lewis, Mark L.; Moreto, Alexander; Transitive permutation groups in which all derangements are involutions. J. Pure Appl. Algebra 207 (2006), no. 3, 717-724.
• Keller, Thomas Michael; Fixed conjugacy classes of normal subgroups and the $k(GV)$-problem. J. Algebra 305 (2006), no. 1, 457--486.
• Isaacs, I. M.; Keller, Thomas Michael; Meierfrankenfeld, U.; Moreto, Alexander; Fixed point spaces, primitive character degrees and conjugacy class sizes. Proc. Amer. Math. Soc. 134 (2006), no. 11, 3123--3130
• Keller, Thomas Michael Inductive arguments for the non-coprime $k(GV)$-problem. Algebra Colloq. 13 (2006), no. 1, 35--39.
• Keller, Thomas Michael; Derived length and conjugacy class sizes. Adv. Math. 199 (2006), no. 1, 88--103.
• Keller, Thomas Michael; The $k(GV)$-problem revisited. J. Aust. Math. Soc. 79 (2005), no. 2, 257--276.
• Keller, Thomas Michael; Ragan, Dustin; Tims, Geoffrey T.; On the Taketa bound for normally monomial $p$-groups of maximal class. J. Algebra 277 (2004), no. 2, 657--688.
• Keller, Thomas Michael; Orbits in finite group actions. Groups St. Andrews 2001 in Oxford. Vol. II, 306--331, London Math. Soc. Lecture Note Ser., 305, Cambridge Univ. Press, Cambridge, 2003.
• Keller, Thomas Michael; A new approach to the $k(GV)$-problem. J. Aust. Math. Soc. 75 (2003), no. 2, 193--219.
• Keller, Thomas Michael; Orbit sizes and character degrees. III. J. Reine Angew. Math. 545 (2002), 1--17.
• Keller, Thomas Michael; On the orbit sizes of permutation groups on the power set. Algebra Colloq. 7 (2000), no. 1, 27--32.
• Keller, Thomas Michael; Orbit sizes and character degrees. II. J. Reine Angew. Math. 516 (1999), 27--114.
• Keller, Thomas Michael Orbit sizes and character degrees. Pacific J. Math. 187 (1999), no. 2, 317--332.
• Keller, Thomas Michael; On the asymptotic Taketa bound for $A$-groups. J. Algebra 191 (1997), no. 1, 127--140.
• Keller, Thomas Michael; A linear bound for $\rho(n)$. J. Algebra 178 (1995), no. 2, 643--652.
• Keller, Thomas Michael; Solvable groups with at most four prime divisors in the element orders. J. Algebra 175 (1995), no. 1, 1--23.
• Keller, Thomas Michael; On the asymptotic behaviour of $\rho(n)$. J. Algebra 174 (1995), no. 2, 587--598.
• Keller, Thomas Michael; Solvable groups with a small number of prime divisors in the element orders. J. Algebra 170 (1994), no. 2, 625--648.

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