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

Published online by Cambridge University Press:  20 November 2018

Olga Macedonska-Nosalska
Olga Macedonska-Nosalska*
Affiliation:
Instytut Matematyki, Politechnika Śalaska Zwyciȩstwa 42 44-100 gliwice, Poland
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Abstract

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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.

Keywords

20E05free groupNielsen transformationautomorphismelementary simultaneous Nielsen transformation

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 2 , 01 June 1985 , pp. 223 - 230
Copyright
Copyright © Canadian Mathematical Society 1985

References

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