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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical notes 61 (1997), S. 399-408 
    ISSN: 1573-8876
    Keywords: mixed Abelian group ; automorphism group ; holomorph ; splittable group ; serving quasisummand ; regulated group ; quasisplittable group ; bounded group
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the paper, sufficient conditions for the splittability of mixed Abelian groups with periodic automorphism groups are established. Classes of mixed splittable Abelian groups with perfect holomorphs are distinguished.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical notes 62 (1997), S. 288-295 
    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
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