Question

What is Cyclic group .........?



Explain .....?​

Answer 1

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Cyclic group

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In group theory, a branch of abstract algebra, a cyclic group or monogenous group is a group that is generated by a single element.[1] That is, it is a set of invertible elements with a single associative binary operation, and it contains an element g such that every other element of the group may be obtained by repeatedly applying the group operation to g or its inverse. Each element can be written as a power of g in multiplicative notation, or as a multiple of g in additive notation. This element g is called a generator of the group.[1]

Every infinite cyclic group is isomorphic to the additive group of Z, the integers. Every finite cyclic group of order n is isomorphic to the additive group of Z/nZ, the integers modulo n. Every cyclic group is an abelian group (meaning that its group operation is commutative), and every finitely generated abelian group is a direct product of cyclic groups.

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Answer 2

⭐Answer ⭐

✔Cyclic Group :-

If G is a Group .and a€G , so , some member like that x €G , can also written as , integral power of a so,

we can to say a is its generated

,

I.e.

G=(a) = { x: x€G}