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Group homomorphisms inducing cohomology monomorphisms
Authors:Pham Anh Minh
Affiliation:Department of Mathematics, Faculty of Science, University of Hue, Dai hoc Khoa hoc, Hue, Vietnam
Abstract:Let $fcolon Gto K$ be a homomorphism of $p$-groups such that
$f^{(n)}colon H^n(K,mathbf Z /p)to H^n(G,mathbf Z/p)$ is injective, for $1le nle 2$. 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.

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