Proposition 5

a) Let G and $G'$ be groups, and let F be an abelian group. Let $\tau : G\rightarrow$ Aut(F) and $u: G'\rightarrow G$ be group homomorphisms. The mapping $u^*:$ Ex$_{\tau}(G,F)\rightarrow$ Ex$_{\tau\circ u}(G',F)$ is a group homomorphism.

b) Let G be a group, and let F and $F'$ be abelian groups. Let $\tau : G\rightarrow$ Aut(F)$,\tau ': G\rightarrow$ Aut(F$'$), and $v: F\rightarrow F'$ be group homomorphisms such that

for $g\in G$ and $f\in F$. The mapping $v_*:$ Ex$_{\tau}(G,F)\rightarrow$ Ex$_{\tau'}(G,F')$ is a group homomorphism.

This follows from the commutativity of the diagrams

${G'}^{\delta}$ // $G'\times G'F\times F^m$ // F

$_uu_{\times u}$ and $v_{\times v}v$

G $^{\delta}$ // $G\times GF'\times {F'}^m$ // $F'$.