School of Mathematics and Statistics - Research Publications

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Start date: 2000 × End date: 2009 × Author: Miller, Charles × Subject: Group Theory and Generalisations; Expanding Knowledge in the Mathematical Sciences ×

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    VIRTUAL PROPERTIES OF CYCLICALLY PINCHED ONE-RELATOR GROUPS
    Baumslag, G ; Fine, B ; Miller, CF ; Troeger, D (WORLD SCIENTIFIC PUBL CO PTE LTD, 2009-03)
    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.