This book contains the proceedings of the conference of the same title held at the Colorado State University in September 2004, coinciding with the 60th birthday of William Kantor. The proceedings contain three survey papers: one by W. Kantor on finite semifields (division algebras that need not be associative), one by E. A. O’Brian about the search for effective algorithms for linear groups, and one by T. Pentilla on applications of computer algebra to finite geometry. Besides these survey papers, there are fifteen research papers exploring deeper interplay between the three main topics of the conference. Among the themes of the papers, one can find Hadamard designs, generalized quadrangles, symplectic translation planes, reduction algorithms for matrix groups, efficient presentations for the Mathieu simple group M22 and its cover, finite primitive permutation groups, etc.

Reviewer:

jtu