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Earn +20 ptsQ: Is every abelian group is cyclic or not?
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Is every abelian group is cyclic or not and why?
every abelian group is not cyclic. e.g, set of (Q,+) it is an abelian group but not cyclic.
Every subgroup of a cyclic group is cyclic?
Yes, every subgroup of a cyclic group is cyclic because every subgroup is a group.
Is every solvable group abelian?
No.
Is the symmetry group of the square an abelian group?
Abelian meaning commutative. If the symmetry group of a square is commutative then it's an abelian group or else it's not.
Proof or Disprove 'If every proper subgroup of G is cyclic then G must be cyclic'?
No! Take the quaternion group Q_8.
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