3 votes 3 votes A group $G$ in which $(a b)^2=a^2 b^2$ for all $a, b$ in $G$ is necessarily finite cyclic abelian none of the above Set Theory & Algebra goclasses2024-mockgate-13 goclasses set-theory&algebra group-theory 1-mark + – GO Classes asked Jan 28 • retagged Jan 28 by Lakshman Bhaiya GO Classes 409 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes If $a b a b=a a b b$, then multiplying by $a^{-1}$ on the left and $b^{-1}$ on the right gives us $b a=a b$. Hence $\text{G}$ is abelian. Abelian Group ALL definitions & variations: Abelian Group - ALL Alternative Definitions | GATE CSE 1988, 2022 GO Classes answered Jan 28 • edited Jan 28 by Deepak Poonia GO Classes comment Share Follow See all 0 reply Please log in or register to add a comment.
