1. bookVolume 33 (2019): Issue 1 (September 2019)
Journal Details
License
Format
Journal
eISSN
2391-4238
ISSN
0860-2107
First Published
01 Jan 1985
Publication timeframe
2 times per year
Languages
English
access type Open Access

Inverse Ambiguous Functions and Automorphisms on Finite Groups

Published Online: 18 Jul 2019
Volume & Issue: Volume 33 (2019) - Issue 1 (September 2019)
Page range: 284 - 297
Received: 22 Nov 2018
Accepted: 12 May 2019
Journal Details
License
Format
Journal
eISSN
2391-4238
ISSN
0860-2107
First Published
01 Jan 1985
Publication timeframe
2 times per year
Languages
English
Abstract

If G is a finite group, then a bijective function f : G → G is inverse ambiguous if and only if f(x)−1 = f−1(x) for all x ∈ G. We give a precise description when a finite group admits an inverse ambiguous function and when a finite group admits an inverse ambiguous automorphism.

Keywords

MSC 2010

[1] Y. Berkovich, Groups of Prime Power Order, Vol. 1, De Gruyter Expositions in Mathematics, 46, Walter de Gruyter GmbH & Co. KG, Berlin, 2008.10.1515/9783110208221Search in Google Scholar

[2] R. Cheng, A. Dasgupta, B.R. Ebanks, L.F. Kinch, L.M. Larson and R.B. McFadden, When does f−1 = 1/f?, Amer. Math. Monthly 105 (1998), no. 8, 704–717.Search in Google Scholar

[3] R. Euler and J. Foran, On functions whose inverse is their reciprocal, Math. Mag. 54 (1981), no. 4, 185–189.10.1080/0025570X.1981.11976923Open DOISearch in Google Scholar

[4] M. Griffiths, f(f(x)) = x, windmills, and beyond, Math. Mag. 83 (2010), no. 1, 15–23.Search in Google Scholar

[5] M. Herzog, Counting group elements of order p modulo p2, Proc. Amer. Math. Soc. 66 (1977), no. 2, 247–250.Search in Google Scholar

[6] H. Kurzweil and B. Stellmacher, The Theory of Finite Groups. An Introduction, Springer-Verlag, New York, 2004.10.1007/b97433Search in Google Scholar

[7] D.J. Schmitz, Inverse ambiguous functions on fields, Aequationes Math. 91 (2017), no. 2, 373–389.Search in Google Scholar

[8] D. Schmitz and K. Gallagher, Inverse ambiguous functions on some finite non-abelian groups, Aequationes Math. 92 (2018), no. 5, 963–973.Search in Google Scholar

[9] R. Schnabel, Elemente der Gruppentheorie, Mathematik für die Lehrerausbildung, B.G. Teubner, Stuttgart, 1984.10.1007/978-3-322-94759-8Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo