# Mathematics

Department of Mathematics
MCS 470
Phone: 512-245-2551
Fax: 512-245-3425
math@txstate.edu

# Keller, Thomas

 Contact Information Thomas Keller, Ph.D. Professor Office: MCS 557 Email: tk04@txstate.edu Phone: 512-245-3735 Fax: 512-245-3425 Research Interest Group theory

Thomas Keller has a Ph.D. in Mathematics from the University of Mainz, is a Professor of Mathematics and has interests in finite group theory. His recent research is on upper and lower bounds for the number of conjugacy classes of a finite group. He also has work dealing 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. Much of his work is based on studying the orbits that are induced by the action of linear groups on finite vector spaces and often involves 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.