# Category:Facts about odd-order p-groups that break down for 2-groups

From Groupprops

This category lists facts that are true for (certain kinds of) finite -groups for odd primes (i.e., for odd-order p-groups) but not for the corresponding finite -groups.

For general facts about finite groups that require the additional assumption of odd order, refer Category:Facts about odd-order groups that break down for even-order groups.

## Pages in category "Facts about odd-order p-groups that break down for 2-groups"

The following 17 pages are in this category, out of 17 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 elementary abelian group is fully invariant in holomorph
- 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