A converse to a residual finiteness theorem of G. Baumslag
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- by M. Shirvani
- Proc. Amer. Math. Soc. 104 (1988), 703-706
- DOI: https://doi.org/10.1090/S0002-9939-1988-0935110-8
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Abstract:
It is shown that if at least two of the factor groups of a nontrivial amalgamated free product $G$ satisfy nontrivial identities, then a special form of the profinite closure of the associated subgroups is necessary (as well as sufficient) for the residual finiteness of $G$. An example shows that the necessity no longer holds if only one of the factor groups satisfies an identity.References
- Gilbert Baumslag, On the residual finiteness of generalised free products of nilpotent groups, Trans. Amer. Math. Soc. 106 (1963), 193–209. MR 144949, DOI 10.1090/S0002-9947-1963-0144949-8
- R. J. Gregorac, On residually finite generalized free products, Proc. Amer. Math. Soc. 24 (1970), 553–555. MR 260878, DOI 10.1090/S0002-9939-1970-0260878-2
- Hanna Neumann, Generalized free products with amalgamated subgroups, Amer. J. Math. 70 (1948), 590–625. MR 26997, DOI 10.2307/2372201
- M. Shirvani, On residually finite HNN-extensions, Arch. Math. (Basel) 44 (1985), no. 2, 110–115. MR 780256, DOI 10.1007/BF01194073
- M. Shirvani, On residually finite graph products, J. Pure Appl. Algebra 49 (1987), no. 3, 281–282. MR 920943, DOI 10.1016/0022-4049(87)90136-8
Bibliographic Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 703-706
- MSC: Primary 20E06; Secondary 20E26
- DOI: https://doi.org/10.1090/S0002-9939-1988-0935110-8
- MathSciNet review: 935110