Next Article in Journal
On the Convolution Quadrature Rule for Integral Transforms with Oscillatory Bessel Kernels
Previous Article in Journal
On Eccentricity-Based Topological Indices and Polynomials of Phosphorus-Containing Dendrimers
Article Menu
Issue 7 (July) cover image

Export Article

Open AccessArticle
Symmetry 2018, 10(7), 238; https://doi.org/10.3390/sym10070238

Fixed Points of Automorphisms of Certain Non-Cyclic p-Groups and the Dihedral Group

1
Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
2
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
Full-Text   |   PDF [275 KB, uploaded 25 June 2018]

Abstract

Let G=ZpZp2, 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 fixing d elements of G and denote it by θ(G,d). 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 ZpaZpb, where a and b are positive integers with a<b. Finally, we compute θ(D2q,d), where D2q is the dihedral group of order 2q, q is an odd prime, and d{1,q,2q}. View Full-Text
Keywords: fixed-point-free automorphism; dihedral group; theta values; unitriangular; Heisenberg group fixed-point-free automorphism; dihedral group; theta values; unitriangular; Heisenberg group
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).
SciFeed

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.

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.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top