Amalgam-characteristic subgroup

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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]

Definition

Definition with symbols

Suppose G is a group and H is a subgroup of G. We say that H is an amalgam-characteristic subgroup of G if H is characteristic in the group L given by:

L = G *_H G.

In other words, L is the amalgam of G with itself over H, and H is treated as the subgroup of L given by the amalgamated H between the two factors.

Relation with other properties

Stronger properties

Weaker properties

Incomparable properties