A faster method to construct extraspecial normaliser subgroups

Abstract

We show how to improve the runtime of the construction of generators of maximal subgroups of $\mathrm{SL}(d,q),\mathrm{SU}(d,q)$ and $\mathrm{Sp}(d,q)$ 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 $O(d^2\log d{\log }^{1+\epsilon }q+{\log }^{2+\epsilon }q)$.

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