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On the number of centralizers and conjugacy class sizes in finite groups.
- Source :
-
Communications in Algebra . 2024, Vol. 52 Issue 8, p3542-3553. 12p. - Publication Year :
- 2024
-
Abstract
- Given a finite group G, denote by cs(G) the set of the sizes of the conjugacy classes of G and by Cent(G) the set of the centralizers of elements of G. Consider a prime p and integers s ≥ 2 and n ≥ 2 , with gcd (p , s) = 1 . In this paper, some relations between cs(G) and | Cent (G) | are established in the case where cs (G) = { 1 , p n , p n − 1 s } . Further, when p ∈ { 2 , 3 } , we determine the values of s and the structure of a finite group G such that cs (G) = { 1 , p n , p n − 1 s } . We also describe the structure of an AC-group G such that [ G : Z (G) ] = 3 n s and | Cent (G) | = 1 + ∑ i = 0 n 3 i , where gcd (3 , s) = 1 . [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE groups
*CLASS size
*FROBENIUS groups
*CONJUGACY classes
*CENT
*INTEGERS
Subjects
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 52
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 177395887
- Full Text :
- https://doi.org/10.1080/00927872.2024.2324304