Newbetuts

What are the values of $a$ and $b$ so that $\Bbb Z_2\times\Bbb Z_3\times\Bbb Z_4\times\Bbb Z_9$ is isomorphic with $\Bbb Z_a\times\Bbb Z_b$?

Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$

Frattini subgroup of a cyclic group which is not a p group for some prime p

All elements in $\mathbb{Z}/n\mathbb{Z}$ are representable as sum of a square and a cube?

Nonzero rationals under multiplication are not a cyclic group

Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group

Why is the abelian group of points on an elliptic curve over a finite field isomorphic to the product of at most two cyclic groups?

Find generator of multiplicative group of $\mathbb{F}_{27}$

Give an example of a noncyclic Abelian group all of whose proper subgroups are cyclic.

What is the relation between 'the order of $x^k = n/{\gcd(k,n)}$' and Lagrange's Theorem?

How many homomorphism are there from $\mathbb{Z}_{20}$ to $\mathbb{Z}_{10}$? [duplicate]

Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?

$p$ prime, Group of order $p^n$ is cyclic iff it is an abelian group having a unique subgroup of order $p$

Homomorphisms between $\Bbb Z_n$ and $\Bbb Z_m$ [closed]

Find the subgroups of A4

Proof that all abelian simple groups are cyclic groups of prime order

$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$

New posts in cyclic-groups

Why $c(a_1 \ a_2 \dots \ a_k)c^{-1}=(c(a_1) c(a_2)… c(a_k))$? [duplicate]

A group with no proper non-trivial subgroups

There does not exist group $G$ such that ${\rm Aut}(G)\cong \mathbb{Z}_n$ (for odd $n$)

What are the values of $a$ and $b$ so that $\Bbb Z_2\times\Bbb Z_3\times\Bbb Z_4\times\Bbb Z_9$ is isomorphic with $\Bbb Z_a\times\Bbb Z_b$?

Show $\langle a^m \rangle \cap \langle a^n \rangle = \langle a^{\operatorname{lcm}(m, n)}\rangle$

Frattini subgroup of a cyclic group which is not a p group for some prime p

All elements in $\mathbb{Z}/n\mathbb{Z}$ are representable as sum of a square and a cube?

Nonzero rationals under multiplication are not a cyclic group

Prove that $\mathbb{R^*}$, the set of all real numbers except $0$, is not a cyclic group

Why is the abelian group of points on an elliptic curve over a finite field isomorphic to the product of at most two cyclic groups?

Find generator of multiplicative group of $\mathbb{F}_{27}$

Give an example of a noncyclic Abelian group all of whose proper subgroups are cyclic.

What is the relation between 'the order of $x^k = n/{\gcd(k,n)}$' and Lagrange's Theorem?

How many homomorphism are there from $\mathbb{Z}_{20}$ to $\mathbb{Z}_{10}$? [duplicate]

Structure of $Gal(\mathbb{Q}(\zeta_{15})/\mathbb{Q})$?

$p$ prime, Group of order $p^n$ is cyclic iff it is an abelian group having a unique subgroup of order $p$

Homomorphisms between $\Bbb Z_n$ and $\Bbb Z_m$ [closed]

Find the subgroups of A4

Proof that all abelian simple groups are cyclic groups of prime order

$(\mathbb{Z}/2^n \mathbb{Z})^*$ is not cyclic Group for $n\geq 3$