Abstract
We determine some relevant structural properties of the group of lattice automorphisms of a nonperiodic modular group.
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Baer, R.: The significance of the system of subgroups for the structure of the group, Amer. J. Math. 61 (1939), 1–44.
Costantini, M., Holmes, C. H. and Zacher, G.: A representation theorem for the group of autoprojectivities of an Abelian p-group of finite exponent, Ann. Mat. Pura Appl. 175(4) (1998), 119–140.
Costantini, M. and Zacher, G.: On the group of autoprojectivities of periodic modular groups, J. Group Theory 1(4) (1998), 369–394.
Dixon, J., du Sautoy, M., Mann, A. and Segal, D.: Analytic Pro-p-groups, Cambridge Univ. Press, Cambridge, 1991.
Dugundy, J.: Topology, Allyn and Bacon, Boston, 1966.
Fuchs, L.: Infinite Abelian Groups I, Academic Press, New York, 1973.
Gasparini, E. and Metelli, C.: On projectivities of Abelian groups of torsionfree rank one, Boll. U.M.I. A3 (1984), 363–371.
Hall, M.: The Theory of Groups, Macmillian, New York, 1959.
Holmes, C.: Automorphisms of the lattice of subgroups of \({\mathbb{Z}}_{p^m } \times {\mathbb{Z}}_{p^n } \), Arch. Math. 51 (1988), 491–495.
Iwasawa, K.: On the structure of infinite M-groups, Japan J. Math. 18 (1943), 709–728.
Ore, O.: Structures and group theory II, Duke Math. J. 4 (1938), 247–269.
Ostendorf, U.: Projektivitätstypen torsionfreier Abelscher Gruppen vom Rang 1, Rend. Sem. Mat. Univ. Padova 86 (1991), 183–191.
Sato, K.: Note on lattice-isomorphisms between Abelian groups and non-Abelian groups, Osaka Math. J. 3 (1951), 215–220.
Schmidt, R.: Subgroup Lattices of Groups, vol. 14, de Gruyter, Berlin, 1994.
Zacher, G.: Una caratterizzazione reticolare della finitezza dell'indice di un sottogruppo in un gruppo, Atti Accad. Naz. Lincei Rend. 69 (1980), 317–323.
Zacher, G.: Sottogruppi normali ed r-omomorfismi completi tra gruppi, Ann. Mat. Pura Appl. 139 (1985), 83–106.
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Constantini, M., Zacher, G. Dedicated to H. Wielandt on the occasion of his 90th birthday. Geometriae Dedicata 85, 197–216 (2001). https://doi.org/10.1023/A:1010313729641
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DOI: https://doi.org/10.1023/A:1010313729641