ISSN:
1573-8876
Keywords:
Abelian group
;
holomorph
;
holomorphic isomorphism
;
characteristic subgroup
;
holomorphic decomposability
;
mixed Abelian group
;
elementary automorphism
;
periodic group
;
divisible group
;
centralizer
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Groups with isomorphic holomorphs are said to be holomorphically isomorphic. The following problems are treated. (1) What Abelian groups have the property that their holomorphic isomorphism implies the isomorphism of the groups themselves? (2) Does holomorphic isomorphism of two groups, one of which is Abelian, imply the commutativity of the other group? Classes of groups are selected for which the answers to these questions are positive.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02360869
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