# Conjugacy functor whose normalizer generates whole group with p'-core

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This article defines a property that can be evaluated for a conjugacy functor on a finite group. |View all such properties

## Contents

## Definition

Suppose is a group, is a prime number, and is a conjugacy functor for . We say that is a **conjugacy functor whose normalizer generates whole group with p'-core** if it satisfies the following equivalent conditions for one (and hence every) -Sylow subgroup of :

- The image of in the quotient is a normal subgroup of .

### Equivalence of definitions

`Further information: equivalence of definitions of conjugacy functor whose normalizer generates whole group with p'-core`

## Related notions

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

conjugacy functor that gives a normal subgroup |

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Conjugacy functor that controls fusion | Conjugacy functor whose normalizer generates whole group with p'-core controls fusion |