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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.

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