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The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous (and therefore Hall) but not locally extensible are constructed. Some open questions are also mentioned.
Cite this article
Karl Auinger, Alexander Bors, Formations of finite groups with the M. Hall property. J. Comb. Algebra 3 (2019), no. 2, pp. 113–152DOI 10.4171/JCA/28