# Category:Embeddability theorems

From Groupprops

This category lists theorems that describe how a certain group (or type of group) can be embedded in another group (or type of group).

## Pages in category "Embeddability theorems"

The following 13 pages are in this category, out of 13 total. The count *includes* redirect pages that have been included in the category. Redirect pages are shown in italics.

### E

- Every finite group is a subgroup of a finite 2-generated group
- Every finite group is a subgroup of a finite simple non-abelian group
- Every finite solvable group is a subgroup of a finite group having subgroups of all orders dividing the group order
- Every group is a subgroup of a complete group
- Every group is a subgroup of a divisible group
- Every group is a subgroup of an acyclic group
- Every group of prime power order is a subgroup of a group of unipotent upper-triangular matrices
- Every group of prime power order is a subgroup of an iterated wreath product of groups of order p
- Every pi-torsion-free nilpotent group can be embedded in a unique minimal pi-powered nilpotent group
- Every torsion-free group is a subgroup of a simple torsion-free group
- Every torsion-free group is a subgroup of a torsion-free group with two conjugacy classes