Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-97-04129-4
MathSciNet review: 1423321
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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. L. Evens, Cohomology of groups, Oxford University Press, 1991. MR 93i:20059

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 20J05

Retrieve articles in all journals with MSC (1991): 20J05


Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-97-04129-4
Received by editor(s): September 7, 1995
Communicated by: Ronald Solomon
Article copyright: © Copyright 1997 American Mathematical Society

American Mathematical Society