Computing normalisers of intransitive groups
Group Theory
2021-12-02 v1
Abstract
The normaliser problem takes as input subgroups and of the symmetric group , and asks one to compute . The fastest known algorithm for this problem is simply exponential, whilst more efficient algorithms are known for restricted classes of groups. In this paper, we will focus on groups with many orbits. We give a new algorithm for the normaliser problem for these groups that performs many orders of magnitude faster than previous implementations in GAP. We also prove that the normaliser problem for the special case is at least as hard as computing the group of monomial automorphisms of a linear code over any field of fixed prime order.
Cite
@article{arxiv.2112.00388,
title = {Computing normalisers of intransitive groups},
author = {Mun See Chang and Christopher Jefferson and Colva M. Roney-Dougal},
journal= {arXiv preprint arXiv:2112.00388},
year = {2021}
}