# Category:Facts about odd-order groups that break down for even-order groups

From Groupprops

This category lists facts that are true for certain kinds of odd-order groups, but are not true for even-order groups satisfying the same conditions.

For a list of facts pertaining specifically to groups of prime power order, refer Category:Facts about odd-order p-groups that break down for 2-groups.

## Pages in category "Facts about odd-order groups that break down for even-order groups"

The following 22 pages are in this category, out of 22 total. The count *includes* redirect pages that have been included in the category. Redirect pages are shown in italics.

### C

### F

### J

### O

- Odd-order and normal rank two for all primes implies Sylow tower
- Odd-order cyclic group equals derived subgroup of holomorph
- Odd-order elementary abelian group is fully invariant in holomorph
- Odd-order implies solvable
- Odd-order p-group implies every irreducible representation has Schur index one
- Omega-1 of maximal among Abelian normal subgroups with maximum rank in odd-order p-group equals omega-1 of centralizer
- Omega-1 of odd-order class two p-group has prime exponent