# Difference between revisions of "Order-dominated subgroup"

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==Definition== | ==Definition== | ||

− | A | + | A [[subgroup]] <math>H</math> of a [[finite group]] <math>G</math> is termed '''order-dominated''' in <math>G</math> if, given any finite subgroup <math>K</math> of <math>G</math> such that the order of <math>H</math> divides the order of <math>K</math>, there exists <math>g \in G</math> such that <math>gHg^{-1} \le K</math>. |

==Relation with other properties== | ==Relation with other properties== |

## Revision as of 21:57, 22 February 2009

Template:Finite subgroup propertyBEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

A subgroup of a finite group is termed **order-dominated** in if, given any finite subgroup of such that the order of divides the order of , there exists such that .

## Relation with other properties

### Stronger properties

- Sylow subgroup:
`For full proof, refer: Sylow implies order-dominated`

### Weaker properties

- Order-conjugate subgroup
- Isomorph-conjugate subgroup
- Prehomomorph-dominated subgroup (when the whole group is finite)