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Generalisation of 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 be a given group and A, B be two subgroups of G which may or may not coincide. A homomorphism μ which maps A onto B is called a partial endomorphism of G. When A coincides with G then we call μ a total endomorphism or as it is usually called an endomorphism of G. If μ* is a partial (or total) endomorphism of a supergroup G* ⊇ G, then we say that μ* extends, or continues, μ when μ* is defined for at least all the elements a ∈ A and moreover aμ = aμ* for all a ∈ A If the partial endomorphism μ is an isomorphic mapping then we speak of a partial automorphism of G.

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 4 , September 1960, pp. 171 - 177
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
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4.Neumann, B. H., and Neumann, Hanna, Extending partial endomorphisms of groups. Proc. London Math. Soc. (3) 2 (1952), 337–348.CrossRefGoogle Scholar