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History. Group theory has three main historical sources: number theory, the theory of algebraic equations, and geometry. The number-theoretic strand was begun by Leonhard Euler, and developed by Gauss's work on modular arithmetic and additive and multiplicative groups related to quadratic fields.
- History
The history of group theory, a mathematical domain studying...
- Group (mathematics)
In mathematics, a group is a set with an operation that...
- History
The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry.
Storia della teoria dei gruppi. La teoria dei gruppi ha tre radici storiche: la teoria delle equazioni algebriche, la teoria dei numeri e la geometria . Eulero, Gauss, Lagrange, Abel e Galois sono stati i primi a indagare nell'area delle teoria dei gruppi.
Nella teoria dei gruppi, una parola è qualsiasi prodotto scritto di elementi di un gruppo e dei loro inversi. Ad esempio, se x, y e z sono elementi di un gruppo G, allora xy, z−1 xzz e y−1 zxx−1 yz−1 sono parole nell'insieme { x , y , z }. Due parole diverse possono avere lo stesso valore in G, [1] o anche in ogni gruppo. [2]
In mathematics, a group is a set with an operation that satisfies the following constraints: the operation is associative and has an identity element, and every element of the set has an inverse element. Many mathematical structures are groups endowed with other properties.
Group theory is the study of groups. Groups are sets equipped with an operation (like multiplication, addition, or composition) that satisfies certain basic properties. As the building blocks of abstract algebra, groups are so general and fundamental that they arise in nearly every branch of mathematics and the sciences.
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially (that is, when the groups in question are realized as geometric ...
