Groupprops, The Group Properties Wiki (pre-alpha)

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From Groupprops

Contents 1 Definition 1.1 Symbol-free definitions 2 Relation with other equivalence relations 2.1 Stronger relations 2.2 Weaker relations

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This article defines an equivalence relation over the collection of subgroups within the same big group

Definition

Symbol-free definitions

Two subgroups of a group are automorphs or automorphic subgroups if there is an automorphism of the whole group that maps one of the subgroups isomorphically to the other one.

Relation with other equivalence relations

Stronger relations

• Equal subgroups
• Isomorphic subgroups

Weaker relations

• Conjugate subgroups