94
Views
0
CrossRef citations to date
0
Altmetric
Research Articles

On the number of centralizers and conjugacy class sizes in finite groups

Pages 3542-3553 | Received 06 Jun 2023, Accepted 14 Feb 2024, Published online: 09 Mar 2024

References

  • Abdollahi, A., Jafarian Amiri, S. M., Hassanabadi, A. M. (2007). Groups with specific number of centralizers. Houston J. Math. 33(1):43–57.
  • Ashrafi, A. R. (2000). On finite groups with a given number of centralizers. Algebra Colloq. 7(2):139–146. DOI: 10.1007/s10011-000-0139-5.
  • Ashrafi, A. R. (2000). Counting the centralizers of some finite groups. Korean J. Comput. Appl. Math. 7:115–124. DOI: 10.1007/BF03009931.
  • Baishya, S. J. (2013). On finite groups with specific number of centralizers. Int. Electron. J. Algebra 13:53–62.
  • Belcastro, S. M., Sherman, G. J. (1994). Counting centralizers in finite groups. Math. Mag. 5:111–114.
  • Bertram, E. A., Herzog, M., Mann, A. (1990). On a graph related to conjugacy classes of groups. Bull. London Math. Soc. 22:569–575. DOI: 10.1112/blms/22.6.569.
  • Beltrán, A., Felipe, M. J. (2009). The structure of groups with three class sizes. J. Group Theory 12:539–553.
  • Camina, A. R., Camina, R. D. (2011). The influence of conjugacy class sizes on the structure of finite groups: a survey. Asian-Eur. J. Math. 4:559–588. DOI: 10.1142/S1793557111000459.
  • Dolfi, S., Jabara, E. (2009). The structure of finite groups of conjugate rank 2. Bull. London Math. Soc. 41:916–926. DOI: 10.1112/blms/bdp072.
  • Grove, L. C. (1997). Groups and Characters. New York: Wiley.
  • Isaacs, I. M. (1970). Groups with many equal classes. Duke Math. J. 37:501–506. DOI: 10.1215/S0012-7094-70-03763-4.
  • Iranmanesh, M. A., Zareian, M. H. (2021). On n-centralizer CA-groups. Commun. Algebra 49(10):4186–4195. DOI: 10.1080/00927872.2021.1916513.
  • Ishikawa, K. (2002). On finite p-groups which have only two conjugacy lengths. Israel J. Math. 129:119–123. DOI: 10.1007/BF02773158.
  • Itô, N. (1953). On finite groups with given conjugate types I. Nagoya Math. 6:17–28. DOI: 10.1017/S0027763000016937.
  • Itô, N. (1970). On finite groups with given conjugate types II. Osaka J. Math. 7:231–251.
  • Jafarian Amiri, S. M., Amiri, M., Rostami, H. (2017). Finite groups determined by the number of element centralizers. Commun. Algebra 45(9):3792–3797. DOI: 10.1080/00927872.2016.1246664.
  • Jafarian Amiri, S. M., Madadi, H., Rostami, H. (2015). On 9-centralizer groups. J. Algebra Appl. 14(1):1550003. DOI: 10.1142/S0219498815500036.
  • Jafarian Amiri, S. M., Madadi, H., Rostami, H. (2018). Groups with exactly ten centralizers. Bull. Iran. Math. Soc. 44:1163–1170. DOI: 10.1007/s41980-018-0079-9.
  • Pezzott, J. C. M., Nakaoka, I. N. (2023). A note on the number of centralizers in finite AC-groups. J. Algebra Appl. 22(7):2350142. DOI: 10.1142/S0219498823501426.
  • Pezzott, J. C. M., Nakaoka, I. N. (2019). On groups whose commuting graph of a transversal is strongly regular. Discrete Math. 342(12):111626. DOI: 10.1016/j.disc.2019.111626.
  • Rebmann, J. (1971). F-Gruppen. Arch. Math. 22:225–230. DOI: 10.1007/BF01222567.
  • Schmidt, R. (1994). Subgroup Lattices of Groups. Berlin: De Gruyter.
  • Schmidt, R. (1970). Zentralisatorverbände endlicher Gruppen. Rend. Sem. Mat. Univ. Padova 44:97–131.
  • The GAP Group. (2013). GAP - Groups, Algorithms, and Programming, Version 4.6.4. http://www.gap-system.org
  • Vahidi, J., Talebi, A. A. (2010). The commuting graphs on groups D2n and Qn. J. Math. Comput. Sci. 1:123–127.
  • Zarrin, M. (2011). Criteria for the solubility of finite groups by its centralizers. Arch. Math. 96:225–226. DOI: 10.1007/s00013-011-0233-6.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.