Definition of abelian in English:



  • (of a group) having members related by a commutative operation (e.g., a×b = b×a).

    • ‘In the same year he generalised von Neumann's spectral theorem to locally compact abelian groups.’
    • ‘He does provide an example of the decomposition of an abelian group into cosets of a subgroup.’
    • ‘After submitting a thesis on abelian functions, he received his doctorate in 1895 from the University of Strasbourg.’
    • ‘Schreier showed that the fundamental group of such a space is always abelian.’
    • ‘Herbrand also worked on field theory considering abelian extensions of algebraic number fields.’
    • ‘Galois, after reading Abel and Jacobi's work, worked on the theory of elliptic functions and abelian integrals.’
    • ‘In 1925 he proved the Krull-Schmidt theorem for decomposing abelian groups of operators.’


Mid 19th century: from N. H. Abel (see Abel, Niels Henrik) + -ian.