Abelian meaning commutative. If the symmetry group of a square is commutative then it's an abelian group or else it's not.
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every abelian group is not cyclic. e.g, set of (Q,+) it is an abelian group but not cyclic.
No.
No.
abelian group
An additive group is an abelian group when it is written using the + symbol for its binary operation.