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Original Articles

Finite groups determined by the number of element centralizers

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Pages 3792-3797 | Received 05 Jan 2016, Published online: 23 Jan 2017

References

  • Abdollahi, A., Jafarian Amiri, S. M., Hassanabadi, A. M. (2007). Groups with specific number of centralizers. Houston J. Math. 33(1):43–57.
  • Abdollahi, A., Akbari, S., Maimani, H. R. (2006). Non-commuting graph of a group. J. Algbera 298(2):468–492.
  • Abdollahi, A., Azad, A., Mohamadi Hasanabadi, A., Zarrin, M. (2010). On the clique numbers of non-commuting graphs of certain groups. Algebra Colloq. 17(4):611–620.
  • Ashrafi, A. R. (2000). On finite groups with a given number of centralizers. Algebra Colloq. 7(2):139–146.
  • Ashrafi, A., Taeri, B. (2005). On finite groups with a certain number of centralizers. J. Appl. Math. Computing 17:217–227.
  • Belcastro, S. M., Sherman, G. J. (1994). Counting centralizers in finite groups. Math. Mag. 5:111–114.
  • Bertram, E. A. (1983). Some applications of graph theory to finite groups. Discrete Math. 44(1):31–43.
  • Chin, A. M. Y. (2005). On noncommuting sets in an extraspecial p-group. J. Group Theory 8(2):189–194.
  • Dolfi, S., Herzog, M., Jabara, E. (2010). Finite groups whose noncentral commuting elements have centralizers of equal size. Bull. Aust. Math Soc. 82(2):293–304.
  • The GAP Group, (2007). GAP-Groups, Algoritms, and Programming, version 4.4.10 (http://www.gap-system.org).
  • Jafarian Amiri, S. M., Madadi, H., Rostami, H. (2015). On 9-centralizer groups. J. Algebra Appl. 14(1): 1550003 (13 pages).
  • Jafarian Amiri, S. M., Amiri, M., Madadi, H., Rostami, H. (2015). Finite groups have even more centralizers. Bull. Iran. Math. Soc. 41(6):1423–1431.
  • Jafarian Amiri, S. M., Rostami, H. (2015). Groups with a few nonabelian centralizers. Publ. Math. Debrecen 87(3–4):429–437.
  • Jafarian Amiri, S. M., Madadi, H., Rostami, H. (2016). On F-groups with central factor of order p4. Math. Slovaca, accepted.
  • Jafarian Amiri, S. M., Amiri, M. (2016). Finite groups in which at least 13 of elements are involutions. J. Algebra Appl. 15(8): 1650184 (14 pages).
  • Miller, G. A., Moreno, H. C. (1903). Nonabelian groups in which every subgroup is abelian. Trans. Amer. Math. Soc. 4:398–404
  • Neumann, B. H. (1976). A problem of Paul Erdos on groups. J. Aust. Math. Soc. 21:467–472.
  • Pyber, L. (1987). The number of pairwise noncommuting elements and the index of the centre in a finite group. J. Lond. Math. Soc. 35(2):287–295.
  • Robinson, D. J. S. (1996). A Course in the Theory of Groups. New York: Springer-Verlag.
  • Schmidt, R. (1970). Zentralisatorverbände endlicher gruppen. Rend. Sem. Mat. Univ. Padova 44:97–131.
  • Thompson, J. G. (1968). Nonsolvable finite groups all of whose local subgroups are solvable (Part I). Bull. Amer. Math. Soc. (NS) 74:383–437.
  • Zarrin, M. (2011). Criteria for the solubility of finite groups by its centralizers. Arch. Math. 96:225–226.
  • Zarrin, M. (2016). On noncommuting sets and centralisers in infinite groups. Bull. Aust. Math. Soc. 93(1):42–46.
  • Zarrin, M. (2013). On solubility of groups with finitely many centralizers. Bull. Iran. Math. Soc. 39:517–521.
  • Zarrin, M. (2015). Derived length and centralizers of groups. J. Algebra Appl. 14(8): 1550133 (4 pages).
  • Zarrin, M. (2009). On element-centralizers in finite groups. Arch. Math. (Basel) 93:497–503.

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