Groups

In mathematics, a group is a collection of elements combined with an operation—such as addition or multiplication—that satisfies four key rules: closure (combining any two elements results in another in the group), associativity (the way elements are grouped doesn’t change the result), an identity element (a special element that leaves others unchanged when combined), and inverses (every element has a counterpart that cancels it out). Groups provide a structured way to understand symmetry, balance, and structure across various mathematical and scientific contexts, from geometry to cryptography.