# Category:Replacement theorems

From Groupprops

This category lists replacement theorems. A replacement theorem is a result that allows one to replace a subgroup satisfying certain properties, with a subgroup satisfying stronger properties, and which is somehow related to the subgroup we started with.

Also see Category:Failures of replacement.

See summary information for various kinds of replacement theorems at collection of groups satisfying a weak normal replacement condition#Examples/facts.

## Pages in category "Replacement theorems"

The following 26 pages are in this category, out of 26 total. The count *includes* redirect pages that have been included in the category. Redirect pages are shown in italics.

### A

- Abelian-to-normal replacement theorem for prime exponent
- Abelian-to-normal replacement theorem for prime-cube index for odd prime
- Abelian-to-normal replacement theorem for prime-cube order
- Abelian-to-normal replacement theorem for prime-fourth order
- Abelian-to-normal replacement theorem for prime-square index

### C

- Congruence condition on number of abelian subgroups of small prime power order and bounded exponent for odd prime
- Congruence condition on number of elementary abelian subgroups of prime-cube and prime-fourth order for odd prime
- Congruence condition on number of elementary abelian subgroups of prime-square order for odd prime
- Corollary of Timmesfeld's replacement theorem for elementary abelian subgroups

### E

### G

### J

- Jonah-Konvisser abelian-to-normal replacement theorem
- Jonah-Konvisser abelian-to-normal replacement theorem for prime-square index
- Jonah-Konvisser congruence condition on number of abelian subgroups of prime-square index for odd prime
- Jonah-Konvisser congruence condition on number of abelian subgroups of small prime power order for odd prime
- Jonah-Konvisser congruence condition on number of elementary abelian subgroups of small prime power order for odd prime
- Jonah-Konvisser elementary abelian-to-normal replacement theorem