Abelian Group - Alternative Definitions | GATE CSE 1988, 2022 | Group Theory | GO Classes | Deepak

Abelian Group - All Alternative Definitions | GATE CSE 1988, GATE CSE 2022 | GO Classes | GATE Overflow | Deepak Poonia Sir

GATE CSE 1988 | Question: 2xviii
Show that if G is a group such that (a.b)2=a2.b2 for all a,b belonging to G, then G is an abelian.
https://gateoverflow.in/94353/Gate-cs...

GATE CSE 2022 | Question: 17
Which of the following statements is/are TRUE for a group G?
If for all x,y∈G,(xy)2=x2y2, then G is commutative.
If for all x∈G,x2=1, then G is commutative. Here, 1 is the identity element of G.
If the order of G is 2, then G is commutative.
If G is commutative, then a subgroup of G need not be commutative.
https://gateoverflow.in/371919/Gate-c...

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