On groups with same number of centralizers

2023/05/28 by Sekhar Jyoti Baishya, Baishya, Sekhar Jyoti
Engineering · Mathematics · #20D60 #20D99 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2305.17621

openalex publication_date 2023/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, among other results, we give some sufficient conditions for every non-abelian subgroup of a group to be isoclinic with the group itself. It is also seen that under certain conditions, two groups have same number of element centralizers implies they are isoclinic. We prove that if G is any group having 4, 5, 7 or 9 element centralizers and H is any non-abelian subgroup of G, then | \Cent(G)|=| \Cent(H)| and G' ≅ H' ≅ C₂, C₃, C₅ or C₇ respectively. Furthermore, it is proved that if G is any group having n ∈ \lbrace 4, 5, 6, 7, 9 \rbrace element centralizers, then | G' |=n-2.

Related

• On the conjecture of groups with the same number of centralizer
• groups with the same number of centralizers
• On groups with a given central factor
• On finite groups with exactly two non-abelian centralizers
• On n-centralizer CA-groups