Some Braces of Cardinality $p^4$ and Related Hopf-Galois Extensions

Abstract

We describe all ${\mathbb{F}}_p$-braces of cardinality $p^4$ which are not right nilpotent. Our solution illustrates a general way of investigating ${\mathbb{F}}_p$-braces of cardinality $p^n$ with a given multiplicative group. The constructed braces are left nilpotent, solvable and prime, and they also contain a non-zero strongly nilpotent ideal.

References in corpus (1)

• Algebraic approach to Rump's results on relations between braces and pre-Lie algebras