On relational complexity and base size of finite primitive groups
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In this paper we show that if G is a primitive subgroup of Sn that is not large base, then any irredundant base for G has size at most 5 log n. This is the first logarithmic bound on the size of an irredundant base for such groups, and is best possible up to a multiplicative constant. As a corollary, the relational complexity of G is at most 5 log n+1, and the maximal size of a minimal base and the height are both at most 5 log n. Furthermore, we deduce that a base for G of size at most 5 log n can be computed in polynomial time.
Kelsey , V & Roney-Dougal , C M 2022 , ' On relational complexity and base size of finite primitive groups ' , Pacific Journal of Mathematics , vol. 318 , no. 1 , pp. 89–108 . https://doi.org/10.2140/pjm.2022.318.89
Pacific Journal of Mathematics
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