A group presentation ${\displaystyle G=(S\mid R)}$ is called aspherical if the two-dimensional CW complex ${\displaystyle K(S\mid R)}$ associated with this presentation is aspherical or, equivalently, if ${\displaystyle \pi _{2}(K(S\mid R))=0}$. The Whitehead conjecture is equivalent to the conjecture that every sub-presentation of an aspherical presentation is aspherical.