Lemieux, Stephane2020-10-162022-05-312022-05-312007Lemieux, S. (2007). Locally finite-indicable groups. COMMUNICATIONS IN ALGEBRA, 35(10), 3195–3198. https://doi.org/10.1080/00914030701410021https://hdl.handle.net/20.500.14078/1943A group is locally ℜ-indicable if every finitely generated subgroup has a nontrivial homomorphism onto a nontrivial ℜ-group. If ℜ is a quasi-variety, then the class L(ℜ) of locally ℜ-indicable groups coincides with the class N(ℜ) of groups which have normal systems with factors in ℜ. It is not known if ℜ must be a quasi-variety in order for the equality L(ℜ) = N(ℜ) to hold. We show here that if ℑ is the class of all finite groups, which is the union of an ascending sequence of quasi-varieties, then L(ℑ) ≠ N(ℑ). Examples of finitely generated groups in L(ℑ)\ N(ℑ) are also constructed.enAll Rights Reservedinfinite alternating grouplocally indicable groupsnormal systemsquasi-varietiesArticlehttps://doi.org/10.1080/00914030701410021