Groups provide structure because of this groups are used to represent phenomena in Physics, Chemistry and Computer Science. This tutorial is focused on giving the basic definitions of different types of groups.
What is a Group?
A group is a set with binary operation. Groups are generally denoted as where is a set and is the binary operation. The binary operation does not need to be multiplication or addition, it needs to be any well defined operation that takes two elements from set and produces one element in set. In order to be considered a group, the set and binary operation must following a list of rules.
- Closure : For all , .
- Identity : There exists element such that for all (For addition the identity is , for multiplication the identity is )
- Associativity : For all ,
- Inverse : For all there exists an element such that .
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