Keller, Thomas

Contact Information
Thomas Keller, Ph.D.

Office: MCS 557
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:

  • (with A. Gruber, M. L. Lewis, K. A. Naughton, B. Strasser) A Characterization of the Prime Graphs of Solvable Groups, J. Algebra 442 (2015), 397–422.
  • (with Y. Yang) Orbits of finite solvable groups on characters, Israel J. Math. 199 (2014), 933–940.
  • Finite groups have even more conjugacy classes, Israel J. Math. 181 (2011), 433--444.
  • Counting characters in linear group actions, Israel J. Math. 171 (2009), 367--384.
  • Fixed conjugacy classes of normal subgroups and the k(GV)-problem, J. Algebra 305, 457-486 (2006).
  • (with I. M. Isaacs, M. L. Lewis, A. Moretó) Transitive permutation groups in which all derangements are involutions, J. Pure Appl. Algebra 207, 717-724 (2006). 
  • Derived length and conjugacy class sizes, Adv. Math 199, 88-103 (2006).                                      
  • The k(GV)-problem revisited, J. Austral. Math. Soc. 79, 257-276 (2005).                  
  • (with D. Ragan and G. T. Tims) On the Taketa bound for normally monomial p-groups of maximal class}, J. Algebra 277, 675-688 (2004).
  • Orbit sizes and character degrees, III, J. reine angew. Math. 545, 1-17 (2002).
  • Orbit sizes and character degrees, II, J. reine angew. Math. 516, 27-114 (1999).
  • Orbit sizes and character degrees, Pacific J. Math. 187, 317-332 (1999).
  • On the asymptotic Taketa bound for A-groups, J. Algebra 191, 127-140 (1997).