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On solubility of groups with finitely many centralizers

Year 2022, Volume: 32 Issue: 32, 241 - 245, 16.07.2022

Igor Lıma Caio Rodrıgues

https://doi.org/10.24330/ieja.1144159

Abstract

In this paper we present a new sufficient condition for a solubility criterion in terms of centralizers of elements. This result is a corrigendum of one of Zarrin's results. Furthermore, we extend some of K. Khoramshahi and M. Zarrin's results in the primitive case.

Keywords

Centralizer $n$-centralizer group simple group

References

  • A. Abdollahi, S. M. Jafarian Amiri and A. M. Hassanabadi, Groups with specific number of centralizers, Houston J. Math., 33(1) (2007), 43-57.
  • A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloq., 7 (2000), 139-146.
  • S. M. Belcastro and G. J. Sherman, Counting centralizers in finite groups, Math. Mag., 67(5) (1994), 366-374.
  • Z. Foruzanfar and Z. Mostaghim, On 10-centralizer groups of odd order, ISRN Algebra 2014, 607984 (4pp).
  • P. Hall, The classification of prime power groups, J. Reine Agnew. Math., 182 (1940), 130-141.
  • S. M. Jafarian Amiri, H. Madadi and H. Rostami, On 9-centralizer groups, J. Algebra Appl., 14 (1) (2015), 1550003 (13 pp).
  • S. M. Jafarian Amiri, H. Madadi and H. Rostami, Groups with exactly ten centralizers, Bull. Iranian Math. Soc., 44 (2018), 1163-1170.
  • K. Khoramshahi and M. Zarrin, Groups with the same number of centralizers, J. Algebra Appl. 20(2) (2021), 2150012 (6 pp).
  • W. M. Potter, Nonsolvable groups with an automorphism inverting many elements, Arch. Math. (Basel), 50 (1998), 292-299.
  • M. Rezaei and Z. Foruzanfar, On primitive 11-centralizer groups of odd order, Malays. J. Math. Sci., 10(3) (2016), 361-368.
  • The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.10.2; 2019. (https://www.gap-system.org)
  • M. Zarrin, On solubility of groups with finitely many centralizers, Bull. Iranian Math. Soc., 39 (2013), 517-521.
  • M. Zarrin, On noncommuting sets and centralisers in infinite groups, Bull. Aust. Math. Soc., 93 (2016), 42-46.

Year 2022, Volume: 32 Issue: 32, 241 - 245, 16.07.2022

Igor Lıma Caio Rodrıgues

https://doi.org/10.24330/ieja.1144159

Abstract

References

  • A. Abdollahi, S. M. Jafarian Amiri and A. M. Hassanabadi, Groups with specific number of centralizers, Houston J. Math., 33(1) (2007), 43-57.
  • A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloq., 7 (2000), 139-146.
  • S. M. Belcastro and G. J. Sherman, Counting centralizers in finite groups, Math. Mag., 67(5) (1994), 366-374.
  • Z. Foruzanfar and Z. Mostaghim, On 10-centralizer groups of odd order, ISRN Algebra 2014, 607984 (4pp).
  • P. Hall, The classification of prime power groups, J. Reine Agnew. Math., 182 (1940), 130-141.
  • S. M. Jafarian Amiri, H. Madadi and H. Rostami, On 9-centralizer groups, J. Algebra Appl., 14 (1) (2015), 1550003 (13 pp).
  • S. M. Jafarian Amiri, H. Madadi and H. Rostami, Groups with exactly ten centralizers, Bull. Iranian Math. Soc., 44 (2018), 1163-1170.
  • K. Khoramshahi and M. Zarrin, Groups with the same number of centralizers, J. Algebra Appl. 20(2) (2021), 2150012 (6 pp).
  • W. M. Potter, Nonsolvable groups with an automorphism inverting many elements, Arch. Math. (Basel), 50 (1998), 292-299.
  • M. Rezaei and Z. Foruzanfar, On primitive 11-centralizer groups of odd order, Malays. J. Math. Sci., 10(3) (2016), 361-368.
  • The GAP Group, GAP - Groups, Algorithms, and Programming, Version 4.10.2; 2019. (https://www.gap-system.org)
  • M. Zarrin, On solubility of groups with finitely many centralizers, Bull. Iranian Math. Soc., 39 (2013), 517-521.
  • M. Zarrin, On noncommuting sets and centralisers in infinite groups, Bull. Aust. Math. Soc., 93 (2016), 42-46.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Igor Lıma This is me

Caio Rodrıgues This is me

Publication Date July 16, 2022
Published in Issue Year 2022 Volume: 32 Issue: 32

Cite

APA Lıma, I., & Rodrıgues, C. (2022). On solubility of groups with finitely many centralizers. International Electronic Journal of Algebra, 32(32), 241-245. https://doi.org/10.24330/ieja.1144159
AMA Lıma I, Rodrıgues C. On solubility of groups with finitely many centralizers. IEJA. July 2022;32(32):241-245. doi:10.24330/ieja.1144159
Chicago Lıma, Igor, and Caio Rodrıgues. “On Solubility of Groups With Finitely Many Centralizers”. International Electronic Journal of Algebra 32, no. 32 (July 2022): 241-45. https://doi.org/10.24330/ieja.1144159.
EndNote Lıma I, Rodrıgues C (July 1, 2022) On solubility of groups with finitely many centralizers. International Electronic Journal of Algebra 32 32 241–245.
IEEE I. Lıma and C. Rodrıgues, “On solubility of groups with finitely many centralizers”, IEJA, vol. 32, no. 32, pp. 241–245, 2022, doi: 10.24330/ieja.1144159.
ISNAD Lıma, Igor - Rodrıgues, Caio. “On Solubility of Groups With Finitely Many Centralizers”. International Electronic Journal of Algebra 32/32 (July 2022), 241-245. https://doi.org/10.24330/ieja.1144159.
JAMA Lıma I, Rodrıgues C. On solubility of groups with finitely many centralizers. IEJA. 2022;32:241–245.
MLA Lıma, Igor and Caio Rodrıgues. “On Solubility of Groups With Finitely Many Centralizers”. International Electronic Journal of Algebra, vol. 32, no. 32, 2022, pp. 241-5, doi:10.24330/ieja.1144159.
Vancouver Lıma I, Rodrıgues C. On solubility of groups with finitely many centralizers. IEJA. 2022;32(32):241-5.