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Embedding Theorems for Groups

Published online by Cambridge University Press:  20 January 2009

C. G. Chehata
C. G. Chehata
Affiliation:
Faculty of Science, The University, Alexandria, Egypt
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By a partial endomorphism of a group G we mean a homomorphic mapping μ of a subgroup A of G onto a subgroup B of G. If μ is denned on the whole of G then it is called a total endomorphism. We call a partial endomorphism totally extendable (or extendable) if there exists a supergroup G*⊇G with a total endomorphism μ* which extends μ in the sense that gμ* = gμ, whenever the right-hand side is defined (3).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 2 , December 1962 , pp. 153 - 157
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

(1) Chehata, C. G., An embedding theorem for groups, Proc. Glasgow Math. Assoc. 4 (1960), 140–143.Google Scholar
(2) Chehata, C. G., Generalisation of an embedding theorem for groups, Proc. Glasgow Math. Assoc., 4 (1960), 171–177.Google Scholar
(3) Neumann, B. H. and Neumann, Hanna, Extending partial endomorphisms of groups, Proc. London Math. Soc. (3) 2 (1952), 337–348.CrossRefGoogle Scholar