On the triviality and non-triviality of the automorphism group of a skew brace

2026/03/18 by Cindy Tsang, Cindy (Sin Yi) Tsang
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory

paper · pdf · doi:10.1515/jgth-2026-0054

Abstract

Abstract It is a simple fact that a group has a trivial automorphism group if and only if it is of order 1 or 2. We prove that the same holds for certain families of skew braces, and given any odd prime 𝑝, we construct a skew brace of order <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mn>2</m:mn> <m:mo>⁢</m:mo> <m:msup> <m:mi>p</m:mi> <m:mn>3</m:mn> </m:msup> </m:mrow> </m:math> 2p³ that has a trivial automorphism group.

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