Abstract
Let \({L(n)}\) be the language of group theory with n additional new constant symbols \({c_1,\ldots,c_n}\). In \({L(n)}\) we consider the class \({{\mathbb{K}}(n)}\) of all finite groups G of exponent \({p > 2}\), where \({G'\subseteq\langle c_1^G,\ldots,c_n^G\rangle \subseteq Z(G)}\) and \({c_1^G,\ldots,c_n^G}\) are linearly independent. Using amalgamation we show the existence of Fraïssé limits \({D(n)}\) of \({{\mathbb{K}}(n)}\). \({D(1)}\) is Felgner’s extra special p-group. The elementary theories of the \({D(n)}\) are supersimple of SU-rank 1. They have the independence property.
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References
Adler, H.: Introduction to theories without the independence property (preprint)
Baudisch A.: A Fraïssé limit of nilpotent groups of finite exponent. Bull. Lond. Math. Soc. 33, 513–519 (2001)
Baudisch A.: Mekler’s construction preserves CM-triviality. Ann. Pure Appl. Log. 115, 115–173 (2002)
Felgner U.: On \({\aleph_0}\)-categorical extra-special p-groups. Logique et Analyse 71–72, 408–428 (1975)
Hodges W.: Model theory. Cambridge University Press, Cambridge (1993)
Kim B., Pillay A.: Simple theories. Ann. Pure Appl. Log. 88, 149–164 (1998)
Macpherson D., Steinhorn C.: One-dimensional asymptotic classes of structures. Trans. Am. Math. Soc. 366, 411–448 (2008)
Shelah S.: Simple unstable theories. Ann. Math. Log. 19, 177–203 (1980)
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Baudisch, A. Neostability-properties of Fraïssé limits of 2-nilpotent groups of exponent \({p > 2}\) . Arch. Math. Logic 55, 397–403 (2016). https://doi.org/10.1007/s00153-015-0456-5
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DOI: https://doi.org/10.1007/s00153-015-0456-5