What is group in discrete mathematics?

Answer 1

A Group is a finite or infinite set of elements with a well defined law of composition defined on its members.

A Group G must satisfy the following propeties:

Closure: If a and b are any two members in G then there is unique element c = ab which is a member of G.

Associative Law: If a b abd c are any three elements of G, then (ab)c = a(bc).

Identity: There is an element, i, in G such that ai = ia = a for all a in G. i is called the identity for G.

Inverse: For every element, a, in G, there is an element in G denoted by a-1 such that aa-1 = a-1a = i.

Note that G need not be commutative ie ab need not be ba.

Answer 2

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Answer 3

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