abélianiser

A technical mathematics verb from group theory: to abelianize a group means to construct its abelianization — the largest commutative (abelian) quotient of the group, formed by dividing out its commutator subgroup. Named after Norwegian mathematician Niels Henrik Abel; used exclusively in algebra, never in everyday French.

• On abélianise le groupe en le quotientant par son sous-groupe des commutateurs. — You abelianize the group by quotienting it by its commutator subgroup.
• Le groupe abélianisé est plus simple à étudier. — The abelianized group is simpler to study.
• Ce cours de master abélianise plusieurs exemples de groupes non commutatifs. — This master's course abelianizes several examples of non-commutative groups.

This is pure technical jargon confined to abstract algebra — the only real pitfall is context: it will only ever come up in a mathematics class or text, never in general conversation, so don't expect to hear it outside that setting.