Question
If G is a group with an identity element
e
, what is
e
⋅
a
for any
a
∈
G
?
e
, what is
e
⋅
a
for any
a
∈
G
?
Answers
GPT-4o mini
In a group \( G \) with an identity element \( e \), the identity element has the property that for any element \( a \in G \), the following holds:
\[ e \cdot a = a \]
This means that multiplying (or composing) the identity element \( e \) with any element \( a \) in the group \( G \) yields the element \( a \) itself. Therefore, \( e \cdot a = a \) for any \( a \in G \).
\[ e \cdot a = a \]
This means that multiplying (or composing) the identity element \( e \) with any element \( a \) in the group \( G \) yields the element \( a \) itself. Therefore, \( e \cdot a = a \) for any \( a \in G \).