VIRTUAL PROPERTIES OF CYCLICALLY PINCHED ONE-RELATOR GROUPS

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    Author
    Baumslag, G; Fine, B; Miller, CF; Troeger, D
    Date
    2009-03-01
    Source Title
    International Journal of Algebra and Computation
    Publisher
    WORLD SCIENTIFIC PUBL CO PTE LTD
    University of Melbourne Author/s
    Miller, Charles
    Affiliation
    Mathematics And Statistics
    Metadata
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    Document Type
    Journal Article
    Citations
    Baumslag, G., Fine, B., Miller, C. F. & Troeger, D. (2009). VIRTUAL PROPERTIES OF CYCLICALLY PINCHED ONE-RELATOR GROUPS. INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION, 19 (2), pp.213-227. https://doi.org/10.1142/S0218196709005032.
    Access Status
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    URI
    http://hdl.handle.net/11343/26714
    DOI
    10.1142/S0218196709005032
    Description

    C1 - Journal Articles Refereed
    Abstract
    We prove that the amalgamated product of free groups with cyclic amalgamations satisfying certain conditions are virtually free-by-cyclic. In case the cyclic amalgamated subgroups lie outside the derived group such groups are free-by-cyclic. Similarly a one-relator HNN-extension in which the conjugated elements either coincide or are independent modulo the derived group is shown to be free-by-cyclic. In general, the amalgamated product of free groups with cyclic amalgamations is free-by-(torsion-free nilpotent). The special case of the double of a free group amalgamating a cyclic subgroup is shown to be virtually free-by-abelian. Analagous results are obtained for certain one-relator HNN-extensions.
    Keywords
    Group Theory and Generalisations; Expanding Knowledge in the Mathematical Sciences

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