Constructing Permutation Representations for Large Matrix Groups

New techniques, both theoretical and practical, are presented for constructing a permutation representation for a matrix group. We assume that the resulting permutation degree, n, can be 10,000,000 and larger. The key idea is to build the new permutation representation using the conjugation action on a conjugacy class of subgroups of prime order. A unique signature for each group element corresponding to the conjugacy class is used in order to avoid matrix multiplication. The requirement of at least n matrix multiplications would otherwise have made the computation hopelessly impractical. Additional software optimizations are described, which reduce the CPU time by at least an additional factor of 10. Further, a special data structure is designed that serves both as a search tree and as a hash array, while re

• Type: Conference
• Year: 1994
• Where: ISSAC
• Authors: Gene Cooperman, Larry Finkelstein, Bryant W. York, Michael Tselman
• Keywords: Conjugacy Class, ISSAC 1994, Mathematics, Matrix Multiplications, Permutation Representation