Every finite group is a subgroup of a finite 2-generated group
From Groupprops
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 , there exists a finite group
containing
such that
is a 2-generated group (?), i.e., the minimum size of generating set of
is at most two.
Facts used
- Every finite group is a subgroup of a finite symmetric group
- Symmetric group on a finite set is 2-generated
Proof
The proof follows by piecing together facts (1) and (2).