A disk-based parallel implementation for direct condensation of large permutation modules

Through the use of a new disk-based method for enumerating very large orbits, condensation for orbits with tens of billions of elements can be performed. The algorithm is novel in that it offers efficient access to data using distributed diskbased data structures. This provides fast access to hundreds of gigabytes of data, which allows for computing without worrying about memory limitations. The new algorithm is demonstrated on one of the longstanding open problems in the Modular Atlas Project [11]: the Brauer tree of the principal 17-block the sporadic simple Fischer group Fi23. The tree is completed by computing three orbit counting matrices for the Fi23-orbit of size 11, 739, 046, 176 acting on vectors of dimension 728 over GF(2). The construction of these matrices requires 3-1/2 days on a cluster of 56 computers, and uses 8 GB of disk storage and 800 MB of memory per machine. Categories and Subject Descriptors

• Type: Conference
• Year: 2007
• Where: ISSAC
• Authors: Eric Robinson, Jürgen Müller 0004, Gene Cooperman
• Keywords: Diskbased Data Structures, ISSAC 2007, Longstanding Open Problems, Orbit Counting Matrices