Subgroup of prime index

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

Symbol-free definition

A subgroup is said to be of prime index in a group if its index in the whole group is a prime number.

Definition with symbols

A subgroup $H$ of a group $G$ is said to be of prime index if $[G:H]$ is a prime number.

Relation with other properties

Stronger properties

• Subgroup of index two

Weaker properties

• Maximal subgroup
• Subgroup of finite index
• Seminormal subgroup