Prove that a group $G$ is abelian if and only if $(ab)^{-1} = a^{-1}b^{-1}$ for all $a, b in G$.
Added by Ryan P.
Close
Step 1
A group \( G \) is abelian if and only if \( ab = ba \) for all \( a, b \in G \). Show more…
Show all steps
Your feedback will help us improve your experience
Sri K and 92 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Let G be a group. Prove that G is abelian if and only if (ab)^3 = a^3b^3 for all a, b ∈ G.
Sri K.
Prove that $A \times B$ is an abelian group if and only if both $A$ and $B$ are abelian.
Nick J.
Prove that if $x^{2}=1$ for all $x \in G$ then $G$ is abelian.
Introduction to Groups
Basic Axioms and Examples
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD
