Fixed Points of Automorphisms of Certain Non-Cyclic p-Groups and the Dihedral Group
Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
Tecnologico de Monterrey, Escuela de Ingeniería y Ciencias, Hidalgo 42080, Mexico
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Received: 27 April 2018 / Revised: 19 June 2018 / Accepted: 20 June 2018 / Published: 25 June 2018
, where p
is a prime number. Suppose that d
is a divisor of the order of G
. In this paper, we find the number of automorphisms of G
elements of G
and denote it by
. As a consequence, we prove a conjecture of Checco-Darling-Longfield-Wisdom. We also find the exact number of fixed-point-free automorphisms of the group
, where a
are positive integers with
. Finally, we compute
is the dihedral group of order
is an odd prime, and
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
Hayat, U.; López-Aguayo, D.; Abbas, A. Fixed Points of Automorphisms of Certain Non-Cyclic p-Groups and the Dihedral Group. Symmetry 2018, 10, 238.
Hayat U, López-Aguayo D, Abbas A. Fixed Points of Automorphisms of Certain Non-Cyclic p-Groups and the Dihedral Group. Symmetry. 2018; 10(7):238.
Hayat, Umar; López-Aguayo, Daniel; Abbas, Akhtar. 2018. "Fixed Points of Automorphisms of Certain Non-Cyclic p-Groups and the Dihedral Group." Symmetry 10, no. 7: 238.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.