Definition: Unvirginal is a concept in mathematics, specifically in number theory and combinatorics. It refers to a set of numbers that do not have any common divisors other than 1. In the context of algebraic structures like groups (specifically, finite groups), an ungrouped set can be defined as one with no elements and no operation. For example, in a group G, if for any two elements a and b in G, there exist integers n and m such that