We present faithful triangular representations of finite Kaluzhnin p-groups P p,n over the field of p elements. This enables us to obtain a triangular representation of the projective limit P p for the groups P p,n . The obtained representation is studied by using the language of matrix templates specially developed for this purpose. As an example, we present a triangular representation of the well-known self-similar Gupta–Sidki 3-group.
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L. A. Kaluzhnin, Selected Chapters of the Group Theory [in Russian], Kiev University, Kiev (1979).
Yu. G. Leonov, “Representation of residually finite 2-groups by infinite-dimensional unitriangular matrices over the field of two elements,” Mat. Stud., 22, No. 2, 134–140 (2004).
Yu. G. Leonov, V. V. Nekrashevich, and V. I. Sushchans’kyi, “Representation of wreath products by unitriangular matrices,” Dopov. Akad. Nauk Ukr., No. 4, 29–33 (2005).
L. A. Kaluzhnin, “La structure des p-groupes de Sylow des groupes symetriques finis,” Ann. Sci. Ecole Norm. Supér, 3(65), 239–276 (1948).
N. Gupta and S. Sidki, “Some infinite p-groups,” Algebra Logika, 22, No. 5, 584–589 (1983).
S. Sidki, “A primitive ring associated to a Burnside 3-group,” J. London Math. Soc., 55, No. 2, 55–64 (1997).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 11, pp. 1501–1511, November, 2011.
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Leonov, Y.G. On the representation of groups approximated by finite p-groups. Ukr Math J 63, 1706–1718 (2012). https://doi.org/10.1007/s11253-012-0607-3
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DOI: https://doi.org/10.1007/s11253-012-0607-3