Obraztsov, Viatcheslav N. Embedding into groups with well-described lattices of subgroups. (English) Zbl 0864.20018 Bull. Aust. Math. Soc. 54, No. 2, 221-240 (1996). The author suggests a new scheme of embedding an arbitrary set of groups into an infinite simple group with a ‘well-described’ lattice of subgroups and a prescribed outer automorphism group. The proof is based on the techniques developed by A. Yu. Ol’shanskij [Geometry of defining relations in groups (1991; Zbl 0676.20014)] and heavily depends on some previous papers of the author and Ol’shanskij. One of the applications of the scheme is a construction (assuming the Continuum Hypothesis) of an uncountable group such that (1) every subgroup is countable, and (2) it embeds every countable group. This improves Shelah’s result who constructed an uncountable group with (1). Reviewer: O.V.Belegradek (Kemerovo) Cited in 1 ReviewCited in 5 Documents MSC: 20F05 Generators, relations, and presentations of groups 20E07 Subgroup theorems; subgroup growth 20F06 Cancellation theory of groups; application of van Kampen diagrams 20E15 Chains and lattices of subgroups, subnormal subgroups 20E32 Simple groups Keywords:group embeddings; infinite simple groups; lattices of subgroups; outer automorphism groups; uncountable groups; countable groups Citations:Zbl 0676.20014 PDFBibTeX XMLCite \textit{V. N. Obraztsov}, Bull. Aust. Math. Soc. 54, No. 2, 221--240 (1996; Zbl 0864.20018) Full Text: DOI References: [1] DOI: 10.1016/S0049-237X(08)71346-6 · doi:10.1016/S0049-237X(08)71346-6 [2] Ol’shanskii, Geometry of defining relations in groups (1989) [3] Ol’shanskii, Vestnik Moskovsk. Univ. 2 pp 28– (1989) [4] DOI: 10.1112/jlms/s1-24.4.247 · Zbl 0034.30101 · doi:10.1112/jlms/s1-24.4.247 [5] DOI: 10.1080/00927879408825167 · Zbl 0836.20033 · doi:10.1080/00927879408825167 [6] Obraztsov, Mat. Sb. 180 pp 529– (1989) [7] DOI: 10.1112/jlms/s1-12.46.120 · Zbl 0016.29501 · doi:10.1112/jlms/s1-12.46.120 [8] Obraztsov, J. Austral. Math. Soc. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.