Group homomorphisms inducing mod-$p$ cohomology monomorphisms
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- by Pham Anh Minh PDF
- Proc. Amer. Math. Soc. 125 (1997), 1577-1578 Request permission
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
- Leonard Evens, The cohomology of groups, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1991. Oxford Science Publications. MR 1144017
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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1577-1578
- MSC (1991): Primary 20J05
- DOI: https://doi.org/10.1090/S0002-9939-97-04129-4
- MathSciNet review: 1423321