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On solubility of groups with finitely many centralizers

Yıl 2022, Cilt: 32 Sayı: 32, 241 - 245, 16.07.2022

Igor Lıma Caio Rodrıgues

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

Öz

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.

Anahtar Kelimeler

Centralizer $n$-centralizer group simple group

Kaynakça

  • 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.

Yıl 2022, Cilt: 32 Sayı: 32, 241 - 245, 16.07.2022

Igor Lıma Caio Rodrıgues

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

Öz

Kaynakça

  • 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.
Toplam 13 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Igor Lıma Bu kişi benim

Caio Rodrıgues Bu kişi benim

Yayımlanma Tarihi 16 Temmuz 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 32 Sayı: 32

Kaynak Göster

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. Temmuz 2022;32(32):241-245. doi:10.24330/ieja.1144159
Chicago Lıma, Igor, ve Caio Rodrıgues. “On Solubility of Groups With Finitely Many Centralizers”. International Electronic Journal of Algebra 32, sy. 32 (Temmuz 2022): 241-45. https://doi.org/10.24330/ieja.1144159.
EndNote Lıma I, Rodrıgues C (01 Temmuz 2022) On solubility of groups with finitely many centralizers. International Electronic Journal of Algebra 32 32 241–245.
IEEE I. Lıma ve C. Rodrıgues, “On solubility of groups with finitely many centralizers”, IEJA, c. 32, sy. 32, ss. 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 (Temmuz 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 ve Caio Rodrıgues. “On Solubility of Groups With Finitely Many Centralizers”. International Electronic Journal of Algebra, c. 32, sy. 32, 2022, ss. 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.