VIRTUAL PROPERTIES OF CYCLICALLY PINCHED ONE-RELATOR GROUPS
AuthorBaumslag, G; Fine, B; Miller, CF; Troeger, D
Source TitleInternational Journal of Algebra and Computation
PublisherWORLD SCIENTIFIC PUBL CO PTE LTD
University of Melbourne Author/sMiller, Charles
AffiliationMathematics And Statistics
Document TypeJournal Article
CitationsBaumslag, 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.
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C1 - Journal Articles Refereed
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.
KeywordsGroup Theory and Generalisations; Expanding Knowledge in the Mathematical Sciences
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