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Existence Theorem for Groups

Published online by Cambridge University Press:  20 January 2009

C. G. Chehata
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Given a partial automorphism of a group G, i.e. an isomorphic mapping μ of a subgroup A of G onto a second subgroup B of G, it is known (2, Theorem I) that there always exists a group H containing G and an inner automorphism of H which extends µ; i.e. there exists an element t of H, such that the transform by t of any element of A is its image under µ.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 4 , December 1963 , pp. 291 - 294
Copyright
Copyright © Edinburgh Mathematical Society 1963

References

REFERENCES

Chehata, C. G.Commutative extension of partial automorphisms of groups, Proc. Glasgow Math. Assoc., 1 (IV) (1953), 170–181.CrossRefGoogle Scholar
Higman, G., Neumann, B. H. and Neumann, H., Embedding theorems for groups, J. London Math. Soc., 24 (1949), 247–254.CrossRefGoogle Scholar