Geodesic
Acentralizers of some Finite Groups
Kragujevac Journal of Mathematics, Tome 49 (2025) no. 2, p. 223

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $G$ be a finite group. The acentralizer of an automorphism $\alpha$ of $G$, is the subgroup of fixed points of $\alpha$, i.e., $C_G(\alpha)= \{g \in G \mid \alpha(g)=g\}$. In this paper we determine the acentralizers of the dihedral group of order $2n$, the dicyclic group of order $4n$ and the symmetric group on $n$ letters. As a result we see that if $n\geq 3$, then the number of acentralizers of the dihedral group and the dicyclic group of order $4n$ are equal. Also we determine the acentralizers of groups of orders $pq$ and $pqr$, where $p$, $q$ and $r$ are distinct primes.
Classification : 20D45, 20D25
Keywords: automorphism, centralizer, acentralizer, finite groups 
Zahra Mozafar; Bijan Taeri. Acentralizers of some Finite Groups. Kragujevac Journal of Mathematics, Tome 49 (2025) no. 2, p. 223 . http://geodesic.mathdoc.fr/item/KJM_2025_49_2_a3/
@article{KJM_2025_49_2_a3,
     author = {Zahra Mozafar and Bijan Taeri},
     title = {Acentralizers of some {Finite} {Groups}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {223 },
     year = {2025},
     volume = {49},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2025_49_2_a3/}
}
TY  - JOUR
AU  - Zahra Mozafar
AU  - Bijan Taeri
TI  - Acentralizers of some Finite Groups
JO  - Kragujevac Journal of Mathematics
PY  - 2025
SP  - 223 
VL  - 49
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KJM_2025_49_2_a3/
LA  - en
ID  - KJM_2025_49_2_a3
ER  - 
%0 Journal Article
%A Zahra Mozafar
%A Bijan Taeri
%T Acentralizers of some Finite Groups
%J Kragujevac Journal of Mathematics
%D 2025
%P 223 
%V 49
%N 2
%U http://geodesic.mathdoc.fr/item/KJM_2025_49_2_a3/
%G en
%F KJM_2025_49_2_a3