Base sizes of primitive groups: bounds with explicit constants

2018/02/20 by Halasi, Zoltan, Liebeck, Martin W., Maroti, Attila · 1 citation
#20B15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1802.06972

Abstract

We show that the minimal base size b(G) of a finite primitive permutation group G of degree n is at most 2 (log |G|/log n) + 24. This bound is asymptotically best possible since there exists a sequence of primitive permutation groups G of degrees n such that b(G) = \lfloor 2 (log |G|/log n) \rceil - 2 and b(G) is unbounded. As a corollary we show that a primitive permutation group of degree n that does not contain the alternating group Alt(n) has a base of size at most max\√(n) , 25\.

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