Commutativity Criterions using Normal Subgroup Lattices

Simion Breaz

Rendiconti del Seminario Matematico della Università di Padova (2009)

  • Volume: 122, page 161-169
  • ISSN: 0041-8994

How to cite

top

Breaz, Simion. "Commutativity Criterions using Normal Subgroup Lattices." Rendiconti del Seminario Matematico della Università di Padova 122 (2009): 161-169. <http://eudml.org/doc/108768>.

@article{Breaz2009,
author = {Breaz, Simion},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Abelian groups; lattices of normal subgroups; commutativity of groups; subgroup lattices},
language = {eng},
pages = {161-169},
publisher = {Seminario Matematico of the University of Padua},
title = {Commutativity Criterions using Normal Subgroup Lattices},
url = {http://eudml.org/doc/108768},
volume = {122},
year = {2009},
}

TY - JOUR
AU - Breaz, Simion
TI - Commutativity Criterions using Normal Subgroup Lattices
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2009
PB - Seminario Matematico of the University of Padua
VL - 122
SP - 161
EP - 169
LA - eng
KW - Abelian groups; lattices of normal subgroups; commutativity of groups; subgroup lattices
UR - http://eudml.org/doc/108768
ER -

References

top
  1. [1] D. ARNOLD, Finite Rank Torsion-Free Abelian Groups and Rings, Lecture Notes in Math., 931 (Springer - Verlag, New-York, 1982). Zbl0493.20034MR665251
  2. [2] R. BRANDL, On groups with certain lattices of normal subgroups, Arch. Math. (Basel), 47 (1986), pp. 6-11. Zbl0599.20036MR855131
  3. [3] S. BREAZ - GR. CǍLUGǍREANU, Every Abelian group is determined by a subgroup lattice, Stud. Sci. Math. Hung., 45 (2008), pp. 135-137. Zbl1156.20024MR2401171
  4. [4] M. CURZIO, Una caratterizzazione reticolare dei gruppi abeliani, Rend. Math. e. Appl., 24 (1965), pp. 1-10. Zbl0171.28404MR194518
  5. [5] L. FUCHS, Infinite Abelian Groups, vol. I, Academic Press, New-York and London, 1970. Zbl0209.05503MR255673
  6. [6] K. GOODEARL, Power cancellation of groups and modules, Pacific J. Math., 64 (1976), pp. 387-411. Zbl0308.16016MR450334
  7. [7] K. A. KEARNES - Á. SZENDREI, Groups with identical subgroup lattices in all powers, J. Group Theory, 7 (2004), pp. 385-402. Zbl1071.20028MR2063404
  8. [8] A. G. KUROSH, The Theory of Groups, Chelsea Publishing Company (NewYork, 1960). Zbl0064.25104MR109842
  9. [9] E. LUKÁCS - P. P. PÁLFY, Modularity of the subgroup lattice of a direct square, Arch. Math. (Basel), 46 (1986), pp. 18-19. Zbl0998.20500MR829806
  10. [10] M. D. MILLER, On the lattice of normal subgroups of a direct product, Pacific J. Math., 60 (1975), pp. 153-158. Zbl0295.20043MR399275
  11. [11] P. P. PÁLFY, Groups and Lattices, Groups St. Andrews 2001 in Oxford. Vol. II, London Math. Soc. Lecture Note Ser., 305, Cambridge Univ. Press (Cambridge, 2003), pp. 428-454. Zbl1085.20508MR2051548
  12. [12] R. SCHMIDT, Subgroup Lattices of Groups, de Gruyter Expositions in Mathematics 14, de Gruyter (Berlin, 1994). Zbl0843.20003MR1292462
  13. [13] E. A. WALKER, Cancellation in direct sums of groups, Proc. A.M.S., 7 (1956), pp. 898-902. Zbl0071.25203MR81440

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.