Category:Replacement theorems
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