Arithmetic in Group Extensions
arXiv:2412.06218 · doi:10.1016/j.jalgebra.2025.09.010
Abstract
We describe a generalization of the concept of a pc presentation that applies to groups with a nontrivial solvable radical. Such a representation can be much more efficient in terms of memory use and even of arithmetic, than permuattion and matrix representations. We illustrate the use of such representations by constructing a maximal subgroup of the sporadic monster group and calculating its -- hitherto unknown -- character table.