# Category:Subgroup metaproperty satisfactions

From Groupprops

*This category lists metaproperty satisfactions over the context space: subgroup. It lists articles which gives the statement, and possibly proof, of a subgroup property satisfying a subgroup metaproperty*

## Pages in category "Subgroup metaproperty satisfactions"

The following 135 pages are in this category, out of 135 total. The count *includes* redirect pages that have been included in the category. Redirect pages are shown in italics.

### 2

### A

### C

- Central factor is centralizer-closed
- Central factor is transitive
- Central factor is upper join-closed
- Central factor satisfies image condition
- Central factor satisfies intermediate subgroup condition
- Characteristically complemented characteristic is transitive
- Characteristicity is centralizer-closed
- Characteristicity is commutator-closed
- Characteristicity is quotient-transitive
- Characteristicity is strongly intersection-closed
- Characteristicity is strongly join-closed
- Characteristicity is transitive
- Characteristicity satisfies partition difference condition
- Cocentrality is transitive
- Cocentrality is upward-closed
- Cocentrality satisfies intermediate subgroup condition
- Commutator-in-center is intersection-closed
- Complemented normal is quotient-transitive
- Complete divisibility-closedness is strongly intersection-closed
- Complete divisibility-closedness is transitive
- Conjugacy-closedness is transitive
- Conjugate-denseness is transitive
- Conjugate-permutability is conjugate-join-closed
- Conjugate-permutability satisfies intermediate subgroup condition
- Contranormality is transitive
- Contranormality is UL-join-closed
- Contranormality is upper join-closed
- Coprime automorphism-faithful characteristicity is transitive

### D

### E

### F

### H

- Hall is transitive
- Hall satisfies intermediate subgroup condition
- Hall satisfies permuting transfer condition
- Homomorph-containment is finite direct power-closed
- Homomorph-containment is quotient-transitive
- Homomorph-containment is strongly join-closed
- Homomorph-containment satisfies intermediate subgroup condition

### I

- Index is multiplicative
- Intermediate automorph-conjugacy is normalizer-closed
- Intermediate characteristicity is quotient-transitive
- Intermediate isomorph-conjugacy is normalizing join-closed
- Intermediately subnormal-to-normal is normalizer-closed
- Isomorph-conjugacy is normalizer-closed in finite
- Isomorph-freeness is quotient-transitive
- Isomorph-freeness is strongly join-closed

### L

### N

- No common composition factor with quotient group is quotient-transitive
- No common composition factor with quotient group is transitive
- Normal Sylow satisfies transfer condition
- Normality is centralizer-closed
- Normality is commutator-closed
- Normality is direct product-closed
- Normality is quotient-transitive
- Normality is strongly intersection-closed
- Normality is strongly join-closed
- Normality is strongly UL-intersection-closed
- Normality is upper join-closed
- Normality satisfies image condition
- Normality satisfies intermediate subgroup condition
- Normality satisfies inverse image condition
- Normality satisfies lower central series condition
- Normality satisfies partition difference condition
- Normality satisfies transfer condition
- Normality-largeness is transitive
- Normality-preserving endomorphism-invariance is finite direct power-closed

### P

- Paranormality is strongly join-closed
- Permutably complemented satisfies intermediate subgroup condition
- Poincare's theorem
- Polynormality is strongly join-closed
- Powering-invariance does not satisfy lower central series condition in nilpotent group
- Powering-invariance is centralizer-closed
- Powering-invariance is commutator-closed in nilpotent group
- Powering-invariance is strongly intersection-closed
- Powering-invariance is strongly join-closed in nilpotent group
- Powering-invariance is transitive
- Powering-invariance is union-closed
- Procharacteristicity is normalizer-closed
- Pronormality is normalizer-closed
- Pronormality is normalizing join-closed
- Pronormality satisfies intermediate subgroup condition
- Pure definability is quotient-transitive
- Pure definability is transitive

### Q

### S

- Strict characteristicity is quotient-transitive
- Strict characteristicity is strongly intersection-closed
- Strict characteristicity is strongly join-closed
- Subhomomorph-containment is transitive
- Subhomomorph-containment satisfies intermediate subgroup condition
- Subnormal-to-normal is normalizer-closed
- Subnormality is finite-relative-intersection-closed
- Subnormality is normalizing join-closed
- Subnormality is permuting join-closed
- Subnormality is permuting upper join-closed in finite
- Subnormality of fixed depth satisfies intermediate subgroup condition
- Subnormality satisfies transfer condition
- Sylow satisfies intermediate subgroup condition
- Sylow satisfies permuting transfer condition