Extension of partial endomorphisms of abelian groups
Glasgow mathematical journal, Tome 6 (1963) no. 1, pp. 45-48
Voir la notice de l'article provenant de la source Cambridge University Press
It is known [1] that for a partial endomorphism μ of a group G that maps the subgroup A ⊆ G onto B ⊆ G. G to be extendable to a total endomorphism μ* of a supergroup G* ⊆ G such that μ an isomorphism on G*(μ*)m for some positive integer m, it is necessary and sufficient that there exist in G a sequence of normal subgroupssuch that L1 ƞA is the kernel of μ andfor ι = 1, 2,..., m–1.The question then arises whether these conditions could be simplified when the group G is abelian. In this paper it is shown not only that the conditions are simplified when Gis abelian but also that the extension group G*⊇G can be chosen as an abelian group.
Chehata, C. G. Extension of partial endomorphisms of abelian groups. Glasgow mathematical journal, Tome 6 (1963) no. 1, pp. 45-48. doi: 10.1017/S2040618500034699
@article{10_1017_S2040618500034699,
author = {Chehata, C. G.},
title = {Extension of partial endomorphisms of abelian groups},
journal = {Glasgow mathematical journal},
pages = {45--48},
year = {1963},
volume = {6},
number = {1},
doi = {10.1017/S2040618500034699},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S2040618500034699/}
}
[1] 1.Chehata, C. G., An embedding theorem for groups, Proc. Glasgow Math. Assoc. 4 (1960), 140–143. Google Scholar | DOI
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