---
tag: 3CAGKW4X10
kind: statement
role: proposition
name: Universal embedding theorem
aliases: [krasner-kaloujnine-embedding-theorem, krasner-kaloujnine-universal-embedding-theorem]
sources:
  - wikipedia: en:61229758@r1304650438
    locator: Universal embedding theorem
    note: adopted
    mention: wikipedia://en/61229758
    sections: [Statement]
same_as:
  wikidata: Q65122664
  wikipedia: Universal embedding theorem
inventory: [XCCX5Z14HJ]
---

## Statement

The **universal embedding theorem**, or **Krasner–Kaloujnine universal embedding theorem**, is a theorem from the mathematical discipline of group theory first published in 1951 by Marc Krasner and Lev Kaluznin. The theorem states that any group extension of a group $H$ by a group $A$ is isomorphic to a subgroup of the regular wreath product $A \operatorname{Wr} H.$ The theorem is named for the fact that the group $A \operatorname{Wr} H$ is said to be *universal* with respect to all extensions of $H$ by $A.$