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  1. Formally, a group is an ordered pair of a set and a binary operation on this set that satisfies the group axioms. The set is called the underlying set of the group, and the operation is called the group operation or the group law . A group and its underlying set are thus two different mathematical objects.

  2. en.wikipedia.org › wiki › Weyl_groupWeyl group - Wikipedia

    Weyl groups in algebraic, group-theoretic, and geometric settings. Above, the Weyl group was defined as a subgroup of the isometry group of a root system. There are also various definitions of Weyl groups specific to various group-theoretic and geometric contexts ( Lie algebra, Lie group, symmetric space, etc.).

  3. If a, b, c, are real numbers (in the ring R) then one has the continuous Heisenberg group H 3 (R). It is a nilpotent real Lie group of dimension 3. In addition to the representation as real 3×3 matrices, the continuous Heisenberg group also has several different representations in terms of function spaces .

  4. Classification of finite simple groups. In mathematics, the classification of finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six or twenty-seven exceptions, called sporadic.

  5. Group cohomology. In mathematics (more specifically, in homological algebra ), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G -module M to elucidate ...

  6. en.wikipedia.org › wiki › B_%E2%88%92_LB − L - Wikipedia

    In particle physics, B − L (pronounced "bee minus ell") is a quantum number which is the difference between the baryon number (B) and the lepton number (L) of a quantum system. Details This quantum number is the charge of a global/gauge U(1) symmetry in B

  7. Haplogroup B (M60) is a human Y-chromosome DNA haplogroup common to paternal lineages in Africa. It is a primary branch of the haplogroup BT. B (M60) is common in parts of Africa, especially the tropical forests of West-Central Africa.

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