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