# hlutgrúpa

## Icelandic[edit]

### Etymology[edit]

From *hlut-* (“partial, sub”) + *grúpa* (“group”), confer *hluti* (“a part”).

### Noun[edit]

**hlutgrúpa** f (*genitive singular* **hlutgrúpu**, *nominative plural* **hlutgrúpur**)

- (group theory) a subgroup; (given a group
*G*under a binary operation *, a subset*H*of*G*is called a subgroup of*G*if*H*also forms a group under the operation *. More precisely,*H*is a subgroup of*G*if the restriction of * to*H*x*H*is a group operation on*H*—*H*≤*G*)

#### Derived terms[edit]

- eiginleg hlutgrúpa (proper subgroup)
- kennileg hlutgrúpa (characteristic subgroup)
- normleg hlutgrúpa (distinguished subgroup, invariant subgroup, normal subgroup)

- óbreytt hlutgrúpa (distinguished subgroup, invariant subgroup, normal subgroup)
- samoka hlutgrúpa (conjugate subgroup)
- Sylow-hlutgrúpa (Sylow subgroup)