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 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.
