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Embedding Theorems for Abelian Groups
Published online by Cambridge University Press: 20 November 2018
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Given an abelian group G and a mapping θ that maps a subgroup A of G homomorphically onto another subgroup B of G, then it is known (3) that there always exists an embedding group G* ⊇ G which is abelian and possesses an endomorphism θ* which coincides with θ on A, i.e. aθ = aθ* whenever aθ is defined. θ is called a partial endomorphism of G and θη a total endomorphism or simply an endomorphism that extends or continues θ.
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- Copyright © Canadian Mathematical Society 1963
References
1.
Chehata, C. G., Embedding theorems for groups, Proc. Edinburgh Math. Soc, 13 (1962), 153–157.Google Scholar
2.
Chehata, C. G., Extension of partial endomorphisms of abelian groups, Proc. Glasgow Math. Assoc, 6 (1963), 45–48.Google Scholar
3.
Neumann, B. H. and Hanna Neumann, Extending partial endomorphisms of groups, Proc. London Math. Soc. (3), 2 (1952), 337–348.Google Scholar
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