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Holt, Derek F.; Rees, Sarah (2017)
Publisher: Mathematical Sciences Publishers
Languages: English
Types: Article
Subjects: QA

Classified by OpenAIRE into

arxiv: Mathematics::Group Theory
We investigate closure results for $\C$-approximable groups, for certain classes $\C$ of groups with invariant length functions. In particular we prove, each time for certain (but not necessarily the same) classes $\C$ that: \linebreak (i) the direct product of two $\C$-approximable groups is $\C$-approximable; (ii) the restricted standard wreath product $G \wr H$ is $\C$-approximable when $G$ is $\C$-approximable and $H$ is residually finite; and (iii) a group $G$ with normal subgroup $N$ is $\C$-approximable when $N$ is $\C$-approximable and $G/N$ is amenable. Our direct product result is valid for LEF, weakly sofic and hyperlinear groups, as well as for all groups that are approximable by finite groups equipped with commutator-contractive invariant length functions (considered in \cite{Thom}). Our wreath product result is valid for weakly sofic groups, and we prove it separately for sofic groups. Our result on extensions by amenable groups is valid for weakly sofic groups, and was proved in \cite[Theorem 1 (3)]{ElekSzabo} for sofic groups $N$. \
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    • [Arzhantseva and Gal 2013] G. Arzhantseva and S. Gal, “On approximation properties of semi-direct products of groups”, preprint, 2013. arXiv
    • [Arzhantseva and Pa˘unescu 2017] G. Arzhantseva and L. Pa˘unescu, “Linear sofic groups and algebras”, Trans. Amer. Math. Soc. 369:4 (2017), 2285-2310. MR Zbl [Brown et al. 2008] N. P. Brown, K. J. Dykema, and K. Jung, “Free entropy dimension in amalgamated free products”, Proc. Lond. Math. Soc. .3/ 97:2 (2008), 339-367. MR Zbl [Capraro and Lupini 2015] V. Capraro and M. Lupini, Introduction to sofic and hyperlinear groups and Connes' embedding conjecture, Lecture Notes in Mathematics 2136, Springer, 2015. MR Zbl [Ciobanu et al. 2014] L. Ciobanu, D. F. Holt, and S. Rees, “Sofic groups: graph products and graphs of groups”, Pacific J. Math. 271:1 (2014), 53-64. MR Zbl
    • [Dixon and Mortimer 1996] J. D. Dixon and B. Mortimer, Permutation groups, Graduate Texts in Mathematics 163, Springer, 1996. MR Zbl
    • [Elek and Szabó 2005] G. Elek and E. Szabó, “Hyperlinearity, essentially free actions and L2- invariants: the sofic property”, Math. Ann. 332:2 (2005), 421-441. MR Zbl [Elek and Szabó 2006] G. Elek and E. Szabó, “On sofic groups”, J. Group Theory 9:2 (2006), 161-171. MR Zbl
    • [Elek and Szabó 2011] G. Elek and E. Szabó, “Sofic representations of amenable groups”, Proc. Amer. Math. Soc. 139:12 (2011), 4285-4291. MR Zbl
    • [Glebsky 2015] L. Glebsky, “Approximation of groups, characterizations of sofic groups, and equations over groups”, preprint, 2015. arXiv
    • [Hayes and Sale 2016] B. Hayes and A. Sale, “The wreath product of two sofic groups is sofic”, preprint, 2016. arXiv
    • [Higman 1951] G. Higman, “A finitely generated infinite simple group”, J. London Math. Soc. .2/ 26 (1951), 61-64. MR Zbl
    • [Pa˘unescu 2011] L. Pa˘unescu, “On sofic actions and equivalence relations”, J. Funct. Anal. 261:9 (2011), 2461-2485. MR Zbl
    • [Pestov and Kwiatkowska 2009] V. G. Pestov and A. Kwiatkowska, “An introduction to hyperlinear and sofic groups”, preprint, 2009. arXiv
    • [Popa 1995] S. Popa, “Free-independent sequences in type II1 factors and related problems”, pp. 187-202 in Recent advances in operator algebras (Orléans, 1992), Astérisque 232, 1995. MR Zbl [Ra˘dulescu 2008] F. Ra˘dulescu, “The von Neumann algebra of the non-residually finite Baumslag group ha; bjab3a 1 D b2i embeds into R!”, pp. 173-185 in Hot topics in operator theory, edited by R. G. Douglas et al., Theta Ser. Adv. Math. 9, Theta, Bucharest, 2008. MR Zbl [Stolz 2013] A. Stolz, “Properties of linearly sofic groups”, preprint, 2013. arXiv [Thom 2012] A. Thom, “About the metric approximation of Higman's group”, J. Group Theory 15:2 (2012), 301-310. MR Zbl
    • [Voiculescu 1998] D. Voiculescu, “A strengthened asymptotic freeness result for random matrices with applications to free entropy”, Internat. Math. Res. Notices 1 (1998), 41-63. MR Zbl Received January 8, 2016. Revised September 25, 2016.
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