<abstract xmlns="http://www.w3.org/1999/xhtml">If <italic>G</italic> is a finite group, then a bijective function <italic>f</italic> : <italic>G → G</italic> is inverse ambiguous if and only if <italic>f</italic>(<italic>x</italic>)−1 = <italic>f</italic>−1(<italic>x</italic>) for all <italic>x ∈ G</italic>. We give a precise description when a finite group admits an inverse ambiguous function and when a finite group admits an inverse ambiguous automorphism.</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.

Inverse Ambiguous Functions and Automorphisms on Finite Groups

Martin-Luther-Universität Halle-Wittenberg

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Inverse Ambiguous Functions and Automorphisms on Finite Groups"}

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...

Inverse Ambiguous Functions and Automorphisms on Finite Groups

Published Online: Jul 18, 2019

Page range: 284 - 297

Received: Nov 22, 2018

Accepted: May 12, 2019

DOI: https://doi.org/10.2478/amsil-2019-0006

Keywords
inverse function, functional equation, finite groups, abelian groups

© 2019 Imke Toborg, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Inverse Ambiguous Functions and Automorphisms on Finite Groups

Published Online: Jul 18, 2019

Page range: 284 - 297

Received: Nov 22, 2018

Accepted: May 12, 2019

DOI: https://doi.org/10.2478/amsil-2019-0006

Keywordsinverse function, functional equation, finite groups, abelian groups

© 2019 Imke Toborg, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
inverse function, functional equation, finite groups, abelian groups