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Embedding Theorems for Abelian Groups

Published online by Cambridge University Press:  20 November 2018

C. G. Chehata
C. G. Chehata*
Affiliation:
The University, Alexandria, Egypt
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 766 - 770
Copyright
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