Quasihomomorphism of groups

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The term quasihomomorphism is used in a number of different contexts, many of them different from this one

WARNING: POTENTIAL TERMINOLOGICAL CONFUSION: Please don't confuse this with quasimorphism
This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]

Definition

Let G and H be groups. A map f:G \to H is termed a quasihomomorphism of groups if it satisfies the following equivalent conditions:

  • Given any homomorphism \varphi:A \to G from an abelian group A to G, the composite f \circ \varphi is a homomorphism from A to H.
  • If a,b \in G commute, then f(ab) = f(a)f(b).

Relation with other properties

Stronger properties

Weaker properties