# Tag Archives: Group Theory

## “Associativity, Left Identity, Left Inverse Elements” Makes a Group

In most undergraduate algebra textbooks, you can find the definition of a group as following: A nonempty set $$G$$ with a binary operation satisfying the following conditions is called a group: Associative rule: $$a(bc)=(ab)c$$ for all $$a,~b,~c \in G$$. Existence of an identity element: There exists $$e\in G$$ s.t. $$ea = ae = a$$ for all \(a \in… Read More »