Yes.
Yes, every subgroup of a cyclic group is cyclic because every subgroup is a group.
every abelian group is not cyclic. e.g, set of (Q,+) it is an abelian group but not cyclic.
Only if it is a square.
No. In fact, a rhombus cannot be cyclic - unless it is a square.
Yes.
Yes, every subgroup of a cyclic group is cyclic because every subgroup is a group.
every abelian group is not cyclic. e.g, set of (Q,+) it is an abelian group but not cyclic.
Only if it is a square.
No. In fact, a rhombus cannot be cyclic - unless it is a square.
No.
Let G be the cyclic group generated by x, say. Ten every elt of G is of the form x^a, for some a
No! Take the quaternion group Q_8.
No, for instance the Klein group is finite and abelian but not cyclic. Even more groups can be found having this chariacteristic for instance Z9 x Z9 is abelian but not cyclic
Every women has a menstructual cycle. It is nothing but a cyclic discharge of every 33 to 39 days
There's a theorem to the effect that every group of prime order is cyclic. Since 5 is prime, the assertion in the question follows from the said theorem.
linear codes and cyclic codes sub class of block codeswhere linear codes satisfies linearity property i.e. addition of any two code vectors produces another valid code vector where as cyclic codes satisfies cyclic shift property i.e. for every cyclic shift of a code vector produces another valid code vector