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Title: Abelian groups have/are near Frattini subgroups (English)
Author: Breaz, Simion
Author: Călugăreanu, Grigore
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 43
Issue: 3
Year: 2002
Pages: 395-405
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Category: math
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Summary: The notions of nearly-maximal and near Frattini subgroups considered by J.B. Riles in [20] and the natural related notions are characterized for abelian groups. (English)
Keyword: nearly maximal subgroup
Keyword: near Frattini subgroup
Keyword: non-near generator
Keyword: DA-groups
Keyword: NDA-groups
Keyword: Richman type
Keyword: functorial subgroup
Keyword: Frattini subgroup
MSC: 20E28
MSC: 20K27
idZBL: Zbl 1068.20058
idMR: MR1920516
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Date available: 2009-01-08T19:23:13Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/119330
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Reference: [1] Allenby R.B.J.T.: Some remarks on the upper Frattini subgroup of a generalized free product.Houston J. Math. 25 (1999), 3 399-403. Zbl 0971.20013, MR 1730890
Reference: [2] Allenby R.B.J.T.: The existence and location of the near Frattini subgroup in certain generalized free products.Houston J. Math. 26 ((2000)), 3 463-468. Zbl 1005.20022, MR 1811933
Reference: [3] Azarian M.K.: On the near Frattini subgroups of certain groups.Houston J. Math. 20 (1994), 3 555-560. Zbl 0817.20028, MR 1287995
Reference: [4] Azarian M.K.: On the near Frattini subgroup.Group Theory (Granville, OH, 1992), pp.21-29, World Sci. Publishing, River Edge, NJ, 1993. Zbl 0896.20019, MR 1348887
Reference: [5] Azarian M.K.: On the near Frattini subgroup of the generalized free product of finitely generated nilpotent groups.Houston J. Math. 23 (1997), 4 613-615. Zbl 0896.20019, MR 1687338
Reference: [6] Azarian M.K.: On the near Frattini subgroups of amalgamated free products with residual properties.Houston J. Math. 23 (1997), 4 603-612. Zbl 0896.20020, MR 1687342
Reference: [7] Charles B.: Sous-groupes fonctoriels et topologies.Studies on Abelian Groups, Paris, 1968, pp.75-92. MR 0240195
Reference: [8] Cutler D.O., Fay T.H.: Radicals of abelian groups.Comm. Algebra 18 (2) (1990), 403-411. Zbl 0697.20045, MR 1047317
Reference: [9] Dlab V.: The Frattini subgroups of abelian groups.Czechoslovak Math. J. 10 (1960), 1-16. Zbl 0093.02801, MR 0114858
Reference: [10] Dugas M., Göbel R.: On radicals and products.Pacific J. Math. 118 (1) (1985), 79-104. MR 0783018
Reference: [11] Dugas M., Oxford E.P.: Preradicals induced by torsion-free abelian groups.Comm. Algebra 17 (4) (1989), 981-1002. Zbl 0668.20042, MR 0990989
Reference: [12] Eda K.: Cardinality restrictions on preradicals.Abelian Group Theory (Perth, 1987), Contemp. Math., 87, Amer. Math. Soc., Providence, RI, 1989, pp.277-283. Zbl 0687.20049, MR 0995283
Reference: [13] Eklof P.C.: Set theoretical methods in homological algebra and abelian groups.Les Presses de l'Université de Montréal, 1980. MR 0565449
Reference: [14] Fay T.H., Oxford E.P., Walls G.L.: Singly generated socles and radicals.Abelian Group Theory, Lecture Notes Math. 1006, Springer, 1983, pp.671-684. Zbl 0522.20039, MR 0722659
Reference: [15] Fedorov Yu.S.: On infinite groups in which all non-trivial subgroups have finite index.Uspekhi Mat. Nauk 1 /6 (1957), 187-189. MR 0041134
Reference: [16] Franciosi S., de Giovanni F.: On groups with many nearly maximal subgroups.Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 9 (1998), 1 19-23. Zbl 0924.20021, MR 1669256
Reference: [17] Fuchs L.: Infinite Abelian Groups, vol. 1 and 2.Academic Press, New York, London, 1970, 1973.
Reference: [18] Göbel R.: On stout and slender groups.J. Algebra 35 (1975), 39-55. MR 0376879
Reference: [19] Lennox J.C., Robinson D.J.S.: Nearly maximal subgroups of finitely generated soluble groups.Arch. Math. Basel 38 (1982), 289-295. MR 0658373
Reference: [20] Riles J.B.: The near Frattini subgroups of infinite groups.J. Algebra 12 (1969), 155-171. Zbl 0182.03702, MR 0238962
Reference: [21] Riles J.B.: The near Frattini subgroups of direct products of groups.J. London Math. Soc. (2) 8 (1974), 239-244. Zbl 0298.20032, MR 0347986
Reference: [22] Shelah S.: On uncountable abelian groups.Israel J. Math. 32 (4) (1979), 311-330. Zbl 0412.20047, MR 0571086
Reference: [23] Stein K.: Analytische Functionen mehrer komplexer Veränderlichen zu vorgegebenen Periodizitätsmoduln und das zweite Cousinsche Problem.Math. Ann. 123 (1951), 201-222. MR 0043219
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