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## Acentralizers of Abelian groups of rank 2

#### Zahar MOZAFAR [1] , Bijan TAERİ [2]

Let $G$ be a group. The Acentralizer of an automorphism $\alpha$ of $G$, is the subgroup of fixed points of $\alpha$, i.e.,  $C_G(\alpha)= \{g\in G \mid \alpha(g)=g\}$. We show that if $G$ is a  finite  Abelian  $p$-group of rank $2$, where $p$ is an odd prime, then the number of Acentralizers of $G$ is exactly the number of subgroups of $G$. More precisely, we show that for each  subgroup $U$ of $G$, there exists an automorphism $\alpha$ of $G$ such that $C_G(\alpha)=U$. Also we find the Acentralizers of infinite two-generator Abelian groups.
Automorphism, centralizer, Acentralizer, finite groups
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Primary Language en Mathematics Mathematics Orcid: 0000-0002-1039-7975Author: Zahar MOZAFAR Institution: Isfahan University of TechnologyCountry: Iran Orcid: 0000-0001-7345-1281Author: Bijan TAERİ Institution: Isfahan University of TechnologyCountry: Iran Publication Date : February 6, 2020
 Bibtex @research article { hujms546988, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {273 - 281}, doi = {10.15672/hujms.546988}, title = {Acentralizers of Abelian groups of rank 2}, key = {cite}, author = {MOZAFAR, Zahar and TAERİ, Bijan} } APA MOZAFAR, Z , TAERİ, B . (2020). Acentralizers of Abelian groups of rank 2. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 273-281 . DOI: 10.15672/hujms.546988 MLA MOZAFAR, Z , TAERİ, B . "Acentralizers of Abelian groups of rank 2". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 273-281 Chicago MOZAFAR, Z , TAERİ, B . "Acentralizers of Abelian groups of rank 2". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 273-281 RIS TY - JOUR T1 - Acentralizers of Abelian groups of rank 2 AU - Zahar MOZAFAR , Bijan TAERİ Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.546988 DO - 10.15672/hujms.546988 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 273 EP - 281 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.546988 UR - https://doi.org/10.15672/hujms.546988 Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics Acentralizers of Abelian groups of rank 2 %A Zahar MOZAFAR , Bijan TAERİ %T Acentralizers of Abelian groups of rank 2 %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/hujms.546988 %U 10.15672/hujms.546988 ISNAD MOZAFAR, Zahar , TAERİ, Bijan . "Acentralizers of Abelian groups of rank 2". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 273-281 . https://doi.org/10.15672/hujms.546988 AMA MOZAFAR Z , TAERİ B . Acentralizers of Abelian groups of rank 2. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 273-281. Vancouver MOZAFAR Z , TAERİ B . Acentralizers of Abelian groups of rank 2. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 281-273.

Authors of the Article
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