On some soluble groups in which U -subgroups form a lattice

Leonid A. Kurdachenko; Igor Ya. Subbotin

Commentationes Mathematicae Universitatis Carolinae (2007)

  • Volume: 48, Issue: 4, page 585-593
  • ISSN: 0010-2628

Abstract

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The article is dedicated to groups in which the set of abnormal and normal subgroups ( U -subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.

How to cite

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Kurdachenko, Leonid A., and Subbotin, Igor Ya.. "On some soluble groups in which $U$-subgroups form a lattice." Commentationes Mathematicae Universitatis Carolinae 48.4 (2007): 585-593. <http://eudml.org/doc/250231>.

@article{Kurdachenko2007,
abstract = {The article is dedicated to groups in which the set of abnormal and normal subgroups ($U$-subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.},
author = {Kurdachenko, Leonid A., Subbotin, Igor Ya.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {abnormal subgroups; $U$-subgroups; counternormal subgroups; abnormal subgroups; counternormal subgroups; lattices of subgroups; soluble groups},
language = {eng},
number = {4},
pages = {585-593},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On some soluble groups in which $U$-subgroups form a lattice},
url = {http://eudml.org/doc/250231},
volume = {48},
year = {2007},
}

TY - JOUR
AU - Kurdachenko, Leonid A.
AU - Subbotin, Igor Ya.
TI - On some soluble groups in which $U$-subgroups form a lattice
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2007
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 48
IS - 4
SP - 585
EP - 593
AB - The article is dedicated to groups in which the set of abnormal and normal subgroups ($U$-subgroups) forms a lattice. A complete description of these groups under the additional restriction that every counternormal subgroup is abnormal is obtained.
LA - eng
KW - abnormal subgroups; $U$-subgroups; counternormal subgroups; abnormal subgroups; counternormal subgroups; lattices of subgroups; soluble groups
UR - http://eudml.org/doc/250231
ER -

References

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  2. Carter R.W., Nilpotent self-normalizing subgroups of soluble groups, Math. Z. 75 (1961), 136-139. (1961) Zbl0168.27301MR0123603
  3. De Falco M., Kurdachenko L.A., Subbotin I.Ya., Groups with only abnormal and subnormal subgroups, Atti Sem. Mat. Fis. Univ. Modena 46 2 (1998), 435-442. (1998) Zbl0918.20017MR1665935
  4. Fatahi A., Groups with only normal and abnormal subgroups, J. Algebra 28 (1974), 15-19. (1974) MR0335628
  5. Kurdachenko L.A., Subbotin I.Ya., On transitivity of abnormality, Publ. Math. Debrecen 61 (2002), 3-4 479-486. (2002) Zbl1012.20030MR1943708
  6. Kurdachenko L.A., Subbotin I.Ya., On U-normal subgroups, Southeast Asian Bull. Math. 26 (2003), 789-801. (2003) Zbl1055.20027MR2045113
  7. Kurdachenko L.A., Subbotin I.Ya., Abnormal subgroups and Carter subgroups in some infinite groups, Algebra Discrete Math. 1 (2005), 69-83. (2005) Zbl1092.20027MR2148821
  8. Kuzennyi N.F., Subbotin I.Ya, New characterization of locally nilpotent ø v e r l i n e I H -groups, Ukrain. Mat. Zh. 40 (1988), 322-326 English translation: Ukrainian Math. J. 40 (1988), 274-277. (1988) MR0952119
  9. Kurosh A.G., The Theory of Groups, American Mathematical Society, Providence, 1979. Zbl0111.02502
  10. Lennox J.C., Robinson D.J.S., The Theory of Infinite Soluble Groups, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2004. Zbl1059.20001MR2093872
  11. Rose J.S., Nilpotent subgroups of finite soluble groups, Math. Z. 106 (1968), 97-112. (1968) Zbl0169.03402MR0252516
  12. Robinson D.J.S., A Course in the Theory of Groups, Springer, New York, 1982. Zbl0836.20001MR0648604
  13. Subbotin I.Ya., Groups with alternatively normal subgroups, Izv. Vyssh. Uchebn. Zaved. Mat. 3 (1992), 86-88 English translation: Soviet. Math. 3 (1992), 87-89. (1992) Zbl0816.20030MR1204823

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