Classification of multiplicative Lie algebra structures on a finite group
Volume 168 / 2022
Colloquium Mathematicum 168 (2022), 25-34
MSC: 15A75, 19C09, 20F12.
DOI: 10.4064/cm8397-12-2020
Published online: 5 August 2021
Abstract
Every multiplicative Lie algebra structure on a group $G$ determines a group homomorphism from the exterior square $G\wedge G$ to $G$. We give a precise characterization of the group homomorphisms $G \wedge G \rightarrow G$ which determine a multiplicative Lie algebra structure on $G$. For certain finite groups, we determine the number of possible images (up to isomorphism) of such structure-defining maps.
