A faster method to construct extraspecial normaliser subgroups

TL;DR

This paper presents an improved algorithm for constructing generators of maximal subgroups related to extraspecial groups in classical groups, significantly reducing computational complexity.

Contribution

The authors develop a faster method for constructing generators of certain maximal subgroups in classical groups, improving previous runtime bounds.

Findings

Runtime reduced from O(d^3 log d log q + log^2 q) to O(d^2 log d log^{1+ε} q + log^{2+ε} q)

Efficient construction of generators for normalisers of extraspecial groups

Applicable to groups like SL, SU, and Sp with large parameters

Abstract

We show how to improve the runtime of the construction of generators of maximal subgroups of $\operatorname{SL}(d, q), \operatorname{SU}(d, q)$ and $\operatorname{Sp}(d, q)$ which arise as normalisers of extraspecial groups or $2$-groups of symplectic type given by Holt and Roney-Dougal (2005) from $O(d^3\log d\log q+\log^2 q)$ to $O(d^2\log d\log^{1+\varepsilon} q+\log^{2+\varepsilon} q)$.