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Group homomorphisms inducing $\operatorname {mod}\text {-}p$
cohomology monomorphisms

Author: Pham Anh Minh
Journal: Proc. Amer. Math. Soc. 125 (1997), 1577-1578
MSC (1991): Primary 20J05
MathSciNet review: 1423321
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Abstract: Let $f\colon G\to K$ 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 $1\le n\le 2$. 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.

References [Enhancements On Off] (What's this?)

  • 1. Leonard Evens, The cohomology of groups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1144017

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Additional Information

Pham Anh Minh
Affiliation: Department of Mathematics, Faculty of Science, University of Hue, Dai hoc Khoa hoc, Hue, Vietnam

Received by editor(s): September 7, 1995
Communicated by: Ronald Solomon
Article copyright: © Copyright 1997 American Mathematical Society