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
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 27 April 2018 / Revised: 19 June 2018 / Accepted: 20 June 2018 / Published: 25 June 2018
PDF [275 KB, uploaded 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
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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.
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