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An embedding theorem for groups

Published online by Cambridge University Press:  18 May 2009

C. G. Chehata
C. G. Chehata
Affiliation:
Faculty of Science, The University Alexandria, Egypt
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Let G by any given group. A homomorphic mapping μ of a subgroup A of G onto a second subgroup B of G, where A and B need not be distinct, is called a partial endomorphism of G. When μ is defined on the whole of G, that is when A = G, we call μ a total endomorphism of G; or simply an endomorphism of G.

A partial (or total) endomorphism μ* of a supergroup G* of G is said to extend (or continue) μ if μ* is defined on a supergroup A* of A, that is, μ* is defined for at least the elements for which μ. is defined, and moreover μ* coincides with μ on A.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 3 , January 1960 , pp. 140 - 143
Copyright
Copyright © Glasgow Mathematical Journal Trust 1960

References

1.Chehata, C. G., Simultaneous extension of partial endomorphisms of groups, Proc. Glasgow Math. Assoc., 2 (1954), 37–46.CrossRefGoogle Scholar
2.Neumann, B. H. and Neumann, Hanna, Extending partial endomorphisms of groups, Proc. London Math. Soc. (3) 2 (1952), 337–348.CrossRefGoogle Scholar