Every finite group is a subgroup of a finite 2-generated group

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This article gives the statement, and possibly proof, of an embeddability theorem: a result that states that any group of a certain kind can be embedded in a group of a more restricted kind.
View a complete list of embeddability theorems

Statement

For any finite group G, there exists a finite group K containing G such that K is a 2-generated group (?), i.e., the minimum size of generating set of K is at most two.

Facts used

  1. Every finite group is a subgroup of a finite symmetric group
  2. Symmetric group on a finite set is 2-generated

Proof

The proof follows by piecing together facts (1) and (2).