Csoports
Csoports, or "groups" in Hungarian, refer to a mathematical structure consisting of a set equipped with an operation that combines any two elements to form a third element, satisfying four fundamental properties: closure, associativity, identity, and invertibility. This concept is foundational in abstract algebra, a branch of mathematics concerned with algebraic structures.
The formal definition of a group requires a set *G* and a binary operation (often denoted as
1. **Closure**: For all *a* and *b* in *G*, the result of the operation *a* ⊙ *b* is
2. **Associativity**: For all *a*, *b*, and *c* in *G*, (*a* ⊙ *b*) ⊙ *c* = *a* ⊙ (*b* ⊙ *c*).
3. **Identity element**: There exists an element *e* in *G* such that for every *a* in *G*,
4. **Inverse element**: For each *a* in *G*, there exists an element *b* in *G* such that
Groups are ubiquitous in mathematics and science, appearing in various contexts such as symmetry operations in
Subgroups are subsets of a group that themselves form a group under the same operation, while quotient