Group homomorphisms inducing mod-p cohomology monomorphisms
Pham Anh Minh
Proc. Amer. Math. Soc. 125 (1997), 1577-1578.

Abstract. Let $f: G \rightarrow H$ be a homomorphism of $p$-groups such that 
$f^{(n)} : H^n(K,Z/p) \rightarrow H^n(G,Z/p)$ is injective, for 
$1 \le n \le 2$. We prove that the non-bijectivity of $f$ implies the 
existence of a quotient $L$ of $G$ containing $K$ as a proper direct factor.
This gives a refined proof of a result of Evens, which asserts that $f$ is 
bijective if $f^{(1)}$ is.