On the embedding of central extensions into wreath products

TL;DR

This paper establishes a necessary condition for embedding central extensions with elementary abelian kernels into wreath products associated with permutation actions, using purely group-theoretic techniques.

Contribution

It introduces a new necessary condition for such embeddings, advancing understanding of the structure of central extensions and wreath products.

Findings

Identifies a necessary condition for embedding central extensions into wreath products.

Uses purely group-theoretic methods for the proof.

Provides insights into the structure of elementary abelian kernels in group embeddings.

Abstract

We find a necessary condition for the embedding of a central extension of a group $G$ with elementary abelian kernel into the wreath product that corresponds to a permutation action of $G$. The proof uses purely group-theoretic methods.