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Simultaneous Extension of Partial Endomorphisms of Groups

Published online by Cambridge University Press:  18 May 2009

C. G. Chehata
C. G. Chehata
Affiliation:
Department of Mathematics, The University, Manchester 13 and Faculty of Science, The University, Alexandria
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Let μ be a homomorphic mapping of some subgroup A of the group G onto a subgroup Ḃ (not necessarily distinct from A) of G; then we call μ a partial endomorphism of G. If A coincides with G, that is, if the homomorphism is defined on the whole of G, we speak of a total endomorphism; this is what is usually called an endomorphism of G. A partial (or total) endomorphism μ*extends or continues a partial endomorphism μ if the domain of μ* contains the domain of μ, that is, μ* is defined for (at least) all those elements for which μ. is defined, and moreover μ* coincides with μ where μ is defined.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 2 , Issue 1 , April 1954 , pp. 37 - 46
Copyright
Copyright © Glasgow Mathematical Journal Trust 1954

References

REFERENCES

(1)Higman, G., Neumann, B. H., and Neumann, H., “Embedding theorems for groups,” J. London Math. Soc., 24 (1949), 247–254.CrossRefGoogle Scholar
(2)Neumann, B. H., and Neumann, Ḣanna, “Extending partial endomorphisms of groups,” Proc. London Math. Soc., (3) 2, (1952), 337–348.CrossRefGoogle Scholar