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On Commutative Continuation of Partial Endomorphisms of Groups

Published online by Cambridge University Press:  20 November 2018

C. G. Chehata
C. G. Chehata*
Affiliation:
Faculty of Science, The University, Alexandria, Egypt
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Given a homomorphic mapping θ of a subgroup A of a group G onto another subgroup B of G, necessary and sufficient conditions for the existence of a supergroup G* of G and an endomorphism θ* of G* such that θ* coincides with θ on A were derived by B. H. Neumann and Hanna Neumann (3). The homomorphism θ is called a partial endomorphism of G and θ* is said to continue, or extend, θ. Necessary and sufficient conditions for the simultaneous continuation of two partial endomorphisms of a group G to total endomorphisms of one supergroup G* ⊇ G were derived by the author (2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 429 - 433
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Chehata, C. G., Commutative extension of partial automorphisms of groups, Proc. Glasgow- Math. Assoc, 1 (1953), 170–81.Google Scholar
2. Chehata, C. G., Simultaneous extension of partial endomorphisms of groups, Proc. Glasgow Math. Assoc, 2 (1954), 37–46.Google Scholar
3. Neumann, B. H. and Hanna Neumann, Extending partial endomorphisms of groups, Proc London Math. Soc (3), 2 (1952), 337–48.Google Scholar
4. Neumann, Hanna, Generalised free products with amalgamated subgroups, Amer. J. Math., 70 (1948), 590–625.Google Scholar