ON THE MONOGENICITY AND GALOIS GROUPS OF x 2 p + a x p + b p x²ᵖ+axᵖ+bᵖbold italic x Superscript bold 2 bold italic p Baseline bold plus bold italic a bold italic x Superscript bold italic p bold plus bold italic b Superscript bold italic p

Let f ( x ) = x 2 p + a x p + b p f(x)=x²ᵖ+axᵖ+bᵖ f left parenthesis x right parenthesis equals x Superscript 2 p Baseline plus a x Superscript p Baseline plus b Superscript p , where p is a prime and a , b ∈ Z a,b∈ Z a comma b element of double struck upper Z with a b ≠ 0 ab≠ 0 a b not equals 0 . If f ( x ) $f(x)$ f left parenthesis x right parenthesis is irreducible over Q Q double struck upper Q , we say that f ( x ) $f(x)$ f left parenthesis x right parenthesis is monogenic if { 1 , θ , θ 2 , … , θ 2 p −