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2 results

  • The Abelian Case of Solitar's Conjecture on Infinite Nielsen Transformations

  • Olga Macedonska-Nosalska
  • Journal:
    Canadian Mathematical Bulletin / Volume 28 / Issue 2 / 01 June 1985
    Published online by Cambridge University Press:
    20 November 2018, pp. 223-230
    Print publication:
    01 June 1985
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  • The paper proves that the group of infinite bounded Nielsen transformations is generated by elementary simultaneous Nielsen transformations modulo the subgroup of those transformations which are equivalent to the identical transformation while acting in a free abelian group. This can be formulated somewhat differently: the group of bounded automorphisms of a free abelian group of countably infinite rank is generated by the elementary simultaneous automorphisms. This proves D. Solitar's conjecture for the abelian case.

  • Note on Automorphisms of a Free Abelian Group

  • Olga Macedońska-Nosalska
  • Journal:
    Canadian Mathematical Bulletin / Volume 23 / Issue 1 / 01 March 1980
    Published online by Cambridge University Press:
    20 November 2018, pp. 111-113
    Print publication:
    01 March 1980
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  • Let F be a free group. Denote by the quotient group by the commutator subgroup which is a free abelian group. The fact that the natural map from Aut(F) into Aut() is an epimorphism, in case when F is finitely generated, was known as a consequence of the theory of Nielsen transformations ([2]) Proposition 4.4 and [3] Corollary 3.5.1).