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  2. Multiplicative group - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_group

    The group scheme of n-th roots of unity is by definition the kernel of the n-power map on the multiplicative group GL(1), considered as a group scheme.That is, for any integer n > 1 we can consider the morphism on the multiplicative group that takes n-th powers, and take an appropriate fiber product of schemes, with the morphism e that serves as the identity.

  3. Multiplicative group of integers modulo n - Wikipedia

    en.wikipedia.org/wiki/Multiplicative_group_of...

    Integer multiplication respects the congruence classes, that is, a ≡ a' and b ≡ b' (mod n) implies ab ≡ a'b' (mod n). This implies that the multiplication is associative, commutative, and that the class of 1 is the unique multiplicative identity. Finally, given a, the multiplicative inverse of a modulo n is an integer x satisfying ax ≡ ...

  4. Symbols of grouping - Wikipedia

    en.wikipedia.org/wiki/Symbols_of_grouping

    If we were to express this idea using symbols of grouping, the factors in a product. Example: 2+3×4 = 2 +(3×4)=2+12=14. In understanding expressions without symbols of grouping, it is useful to think of subtraction as addition of the opposite, and to think of division as multiplication by the reciprocal.

  5. Order of operations - Wikipedia

    en.wikipedia.org/wiki/Order_of_operations

    For example, multiplication is granted a higher precedence than addition, and it has been this way since the introduction of modern algebraic notation. [2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9.

  6. Free group - Wikipedia

    en.wikipedia.org/wiki/Free_group

    Each vertex represents an element of the free group, and each edge represents multiplication by a or b. In mathematics, the free group F S over a given set S consists of all words that can be built from members of S, considering two words to be different unless their equality follows from the group axioms (e.g. st = suu −1 t but s ≠ t −1 ...

  7. Glossary of group theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_group_theory

    The group consists of the finite strings (words) that can be composed by elements from A, together with other elements that are necessary to form a group. Multiplication of strings is defined by concatenation, for instance (abb) • (bca) = abbbca. Every group (G, •) is basically a factor group of a free group generated by G.

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