On the base size and minimal degree of transitive groups

Abstract Let 𝐺 be a permutation group, with minimal degree <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>μ</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:math> \mu(G) and base size <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>b</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy="false">(</m:mo> <m:mi>G</m:mi> <m:mo stretchy="false">)</m:mo> </m:mrow> </m:mrow> </m:mat