Is a group an ordered pair?

Yes, a group is an ordered pair: the first element of the pair is a set (the underlying function of the group), and the second is a binary function on that set (which, in set theory, is actually a set too).

What is operation group Theory?

In mathematics, a group is a set equipped with an operation that combines any two elements to form a third element while being associative as well as having an identity element and inverse elements. These three conditions, called group axioms, hold for number systems and many other mathematical structures.

What is order of a group if the group has four elements?

Answer:All elements in such a group have order 1,2 or 4. If there’s an element with order 4, we have a cyclic group – which is abelian. Otherwise, all elements ≠e have order 2, hence there are distinct elements a,b,c such that {e,a,b,c}=G.

What is an ordered pair of elements?

An ordered pair consists of two numbers that are written in the fixed order. So, we can define an ordered pair as the pair of elements that occur in a particular order and are enclosed in brackets.

What makes an ordered pair?

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. The numeric values in an ordered pair can be integers or fractions.

What is order of group in chemistry?

The number of elements h is called the order of the group. The elements must satisfy the group property that the combination of any pair of elements is also an element of the group.

What is a group defined?

(Entry 1 of 2) 1 : two or more figures forming a complete unit in a composition went there as a group. 2a : a number of individuals assembled together or having some unifying relationship a study group. b : an assemblage of objects regarded as a unit one of the food groups.

Are groups of order 4 cyclic?

From Group whose Order equals Order of Element is Cyclic, any group with an element of order 4 is cyclic. From Cyclic Groups of Same Order are Isomorphic, no other groups of order 4 which are not isomorphic to C4 can have an element of order 4.

What is called ordered pair?

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.