Abelian groups have/are near Frattini subgroups

Simion Breaz; Grigore Călugăreanu

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 3, page 395-405
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Breaz, Simion, and Călugăreanu, Grigore. "Abelian groups have/are near Frattini subgroups." Commentationes Mathematicae Universitatis Carolinae 43.3 (2002): 395-405. <http://eudml.org/doc/248997>.

@article{Breaz2002,
abstract = {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.},
author = {Breaz, Simion, Călugăreanu, Grigore},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nearly maximal subgroup; near Frattini subgroup; non-near generator; DA-groups; NDA-groups; Richman type; functorial subgroup; Frattini subgroup; near Frattini subgroups; non-near generators; nearly maximal subgroups; DA-groups; NDA-groups; Richman types; functorial subgroups},
language = {eng},
number = {3},
pages = {395-405},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Abelian groups have/are near Frattini subgroups},
url = {http://eudml.org/doc/248997},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Breaz, Simion
AU - Călugăreanu, Grigore
TI - Abelian groups have/are near Frattini subgroups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 3
SP - 395
EP - 405
AB - 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.
LA - eng
KW - nearly maximal subgroup; near Frattini subgroup; non-near generator; DA-groups; NDA-groups; Richman type; functorial subgroup; Frattini subgroup; near Frattini subgroups; non-near generators; nearly maximal subgroups; DA-groups; NDA-groups; Richman types; functorial subgroups
UR - http://eudml.org/doc/248997
ER -

References

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  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. (1999) Zbl0971.20013MR1730890
  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. ((2000)) Zbl1005.20022MR1811933
  3. Azarian M.K., On the near Frattini subgroups of certain groups, Houston J. Math. 20 (1994), 3 555-560. (1994) Zbl0817.20028MR1287995
  4. Azarian M.K., On the near Frattini subgroup, Group Theory (Granville, OH, 1992), pp.21-29, World Sci. Publishing, River Edge, NJ, 1993. Zbl0896.20019MR1348887
  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. (1997) Zbl0896.20019MR1687338
  6. Azarian M.K., On the near Frattini subgroups of amalgamated free products with residual properties, Houston J. Math. 23 (1997), 4 603-612. (1997) Zbl0896.20020MR1687342
  7. Charles B., Sous-groupes fonctoriels et topologies, Studies on Abelian Groups, Paris, 1968, pp.75-92. MR0240195
  8. Cutler D.O., Fay T.H., Radicals of abelian groups, Comm. Algebra 18 (2) (1990), 403-411. (1990) Zbl0697.20045MR1047317
  9. Dlab V., The Frattini subgroups of abelian groups, Czechoslovak Math. J. 10 (1960), 1-16. (1960) Zbl0093.02801MR0114858
  10. Dugas M., Göbel R., On radicals and products, Pacific J. Math. 118 (1) (1985), 79-104. (1985) MR0783018
  11. Dugas M., Oxford E.P., Preradicals induced by torsion-free abelian groups, Comm. Algebra 17 (4) (1989), 981-1002. (1989) Zbl0668.20042MR0990989
  12. Eda K., Cardinality restrictions on preradicals, Abelian Group Theory (Perth, 1987), Contemp. Math., 87, Amer. Math. Soc., Providence, RI, 1989, pp.277-283. Zbl0687.20049MR0995283
  13. Eklof P.C., Set theoretical methods in homological algebra and abelian groups, Les Presses de l'Université de Montréal, 1980. MR0565449
  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. Zbl0522.20039MR0722659
  15. Fedorov Yu.S., On infinite groups in which all non-trivial subgroups have finite index, Uspekhi Mat. Nauk 1 /6 (1957), 187-189. (1957) MR0041134
  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. (1998) Zbl0924.20021MR1669256
  17. Fuchs L., Infinite Abelian Groups, vol. 1 and 2, Academic Press, New York, London, 1970, 1973. 
  18. Göbel R., On stout and slender groups, J. Algebra 35 (1975), 39-55. (1975) MR0376879
  19. Lennox J.C., Robinson D.J.S., Nearly maximal subgroups of finitely generated soluble groups, Arch. Math. Basel 38 (1982), 289-295. (1982) MR0658373
  20. Riles J.B., The near Frattini subgroups of infinite groups, J. Algebra 12 (1969), 155-171. (1969) Zbl0182.03702MR0238962
  21. Riles J.B., The near Frattini subgroups of direct products of groups, J. London Math. Soc. (2) 8 (1974), 239-244. (1974) Zbl0298.20032MR0347986
  22. Shelah S., On uncountable abelian groups, Israel J. Math. 32 (4) (1979), 311-330. (1979) Zbl0412.20047MR0571086
  23. Stein K., Analytische Functionen mehrer komplexer Veränderlichen zu vorgegebenen Periodizitätsmoduln und das zweite Cousinsche Problem, Math. Ann. 123 (1951), 201-222. (1951) MR0043219

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