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Commutative Extension of Partial Automorphisms of Groups

Published online by Cambridge University Press:  18 May 2009

C. G. Chehata
C. G. Chehata
Affiliation:
Department of Mathematics, The University, Manchester, and Faculty of Science, The University, Alexandria
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Let μ be an isomorphism which maps a subgroup A of the group G onto a second subgroup B (not necessarily distinct from A) of G; then μ is called a partial automorphism of G. If A coincides with G, that is if the isomorphism is defined on the whole of G, we speak of a total automorphism; this is what is usually called an automorphism of G. A partial (or total) automorphism μ,* extends or continues a partial automorphism μ if 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 1 , Issue 4 , December 1953 , pp. 170 - 181
Copyright
Copyright © Glasgow Mathematical Journal Trust 1953

References

REFERENCES

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