Cyclic complementary extensions and skew-morphism

Abstract A cyclic complementary extension of a finite group 𝐴 is a finite group 𝐺 which contains 𝐴 and a cyclic subgroup 𝐶 such that <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mrow> <m:mi>A</m:mi> <m:mo>∩</m:mo> <m:mi>C</m:mi> </m:mrow> <m:mo>=</m:mo> <m:mrow> <m:mo stretchy="false">{</m:mo> <m:msub> <m:mn>1</m:mn> <m:mi>G</m:mi> </m:msub> <m:mo stretchy="false">}</m:mo> </m:mrow> </m:mrow> </m:math> A\cap C=\{1_{G}\} and <m:math xmlns:m="http://www.w3.org/1998/Math/Ma