Generalized autocommuting probability of a finite group relative to its subgroups

Parama DUTTA; Rajat NATH

doi:https://doi.org/10.15672/hujms.568258

Makale detayları

Generalized autocommuting probability of a finite group relative to its subgroups

Yazarlar:

Parama DUTTA | Rajat NATH

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 1, pp.389-398

Belge Tipi:

Makale

Yayın Tarihi:

2/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000451299

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.568258

Özet:

 

Let H⊆KH⊆KH \subseteq K be two subgroups of a finite group GGG  and Aut(K)Aut(K)\mathrm{Aut}(K) the automorphism group of  KKK. In this paper, we consider the generalized autocommuting probability of GGG relative to its subgroups HHH and KKK, denoted by  Prg(H,Aut(K))Prg(H,Aut(K)){Pr}_g(H,\mathrm{Aut}(K)), which is the probability  that the autocommutator of a randomly chosen pair of elements, one from HHH and the other from Aut(K)Aut(K)\mathrm{Aut}(K), is equal to a given element g∈Kg∈Kg \in K. We study several properties as well as obtain several computing formulae of  this probability. As applications of the computing formulae, we also obtain several  bounds for Prg(H,Aut(K))Prg(H,Aut(K)){Pr}_g(H,\mathrm{Aut}(K)) and characterizations of some finite groups through Prg(H,Aut(K))Prg(H,Aut(K)){Pr}_g(H,\mathrm{Aut}(K)).

Makale detayları

Generalized autocommuting probability of a finite group relative to its subgroups

Yazarlar: Parama DUTTA | Rajat NATH

Yayıncı: Hacettepe University

Ana Başlıklar: Matematik

Dergi: Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 1, pp.389-398

Belge Tipi: Makale

Yayın Tarihi: 2/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000451299

Sıklık: İki Aylık

eISSN: 2651-477X

pISSN: 2651-477X

DOI: https://doi.org/10.15672/hujms.568258

Sayı

Yazarlar:

Parama DUTTA | Rajat NATH

Yayıncı:

Hacettepe University

Ana Başlıklar:

Matematik

Dergi:

Hacettepe Journal of Mathematics and Statistics 2020 Vol.49 Issue 1, pp.389-398

Belge Tipi:

Makale

Yayın Tarihi:

2/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000451299

Sıklık:

İki Aylık

eISSN:

2651-477X

pISSN:

2651-477X

DOI:

https://doi.org/10.15672/hujms.568258