Normalisers of primitive permutation groups in quasipolynomial time
Copyright policy )Normalisers of primitive permutation groups in quasipolynomial time
We show that given generators for subgroups $G$ and $H$ of $\mathrm{S}_n$, if $G$ is primitive then generators for $\mathrm{N}_H(G)$ may be computed in quasipolynomial time, namely $2^{O(\log^3 n)}$. The previous best known bound was simply exponential.
11 pages
- RWTH Aachen University Germany
- University of St Andrews United Kingdom
FOS: Computer and information sciences, F.2.2; G.2.1, T-NDAS, G.2.1, Group Theory (math.GR), Computational Complexity (cs.CC), Computational methods for problems pertaining to group theory, 004, Primitive groups, Computer Science - Computational Complexity, 20B15 (Primary) 20B40, 68W30 (Secondary), FOS: Mathematics, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), QA Mathematics, F.2.2, BDC, QA, Mathematics - Group Theory, R2C
FOS: Computer and information sciences, F.2.2; G.2.1, T-NDAS, G.2.1, Group Theory (math.GR), Computational Complexity (cs.CC), Computational methods for problems pertaining to group theory, 004, Primitive groups, Computer Science - Computational Complexity, 20B15 (Primary) 20B40, 68W30 (Secondary), FOS: Mathematics, Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.), QA Mathematics, F.2.2, BDC, QA, Mathematics - Group Theory, R2C
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