In mathematics, a group is an algebraic structure consisting of a set of elements equipped with an operation that combines any two elements to form a third element. The operation satisfies four conditions called the group axioms, namely closure, associativity, identity and invertibility. One of the most familiar examples of a group is the set of integers together with the addition operation, but the abstract formalization of the group axioms, detached as it is from the concrete nature of any particular group and its operation, applies much more widely. It allows entities with highly diverse mathematical origins in abstract algebra and beyond to be handled in a flexible way while retaining their essential structural aspects. The ubiquity of groups in numerous areas within and outside mathematics makes them a central organizing principle of contemporary mathematics. 

Groups share a fundamental kinship with the notion of symmetry. For example, a symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other. Lie groups are the symmetry groups used in the Standard Model of particle physics; Point groups are used to help understand symmetry phenomena in molecular chemistry; and Poincaré groups can express the physical symmetry underlying special relativity. QUESTIONS:

Q1:
1. What does a group refer to in math?
2. What does a group mean in the context of mathematics?
3. 
Q2:
1. What is contained in a group?
2. What is the pair in a group?
3. 
Q3:
1. Does a group merge two elements to form a third?
2. In a group, is a third element made by merging two?
3. 
Q4:
1. How many conditions do groups meet?
2. What is the number of conditions met by a group?
3. 
Q5:
1. What are the four conditions?
2. What four conditions are listed?
3. 
Q6:
1. What are groups similar to the notion of?
2. What notion is like that of a group?
3. 
Q7:
1. What features are in a symmetry group?
2. What does a symmetry group contain?
3. 
Q8:
1. What does one use point groups to figure out?
2. What can using point groups illuminate?
3. 
Q9:
1. Are groups ubiquitous in few areas?
2. Is the ubiquity of groups described as being in few areas?
3. 
Q10:
1. What is the definition of a group axiom?
2. What can a group axiom be defined as?
3. 
Q11:
1. Is a group axiom detached from the group?
2. Is there a separation between a group axiom and the group?
3. 
