Let $G=\Bbb Z\oplus \Bbb Z$ and $H=\left$. Determine the order of the factor group $G/H$.
33025
What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
117468
$o(g^{k})=\frac{o(g)}{\gcd(o(g),k)}$ order of a power of a group element.
7967
Prove that the order of the cyclic subgroup $\langle g^k\rangle $ is $n/{\operatorname{gcd}(n,k)}$
83178
Matrix Group induction proof and order of elements question
126098
Isomorphism of factor groups
21568
Maximal order of an element in a symmetric group
45310
If $H\leq Z (G)$ and $G/H$ is nilpotent, then $G$ is nilpotent.
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
5069
$GL_n(\mathbb F_q)$ has an element of order $q^n-1$
101602
consider the group $G=\mathbb Q/\mathbb Z$. For $n>0$, is there a cyclic subgroup of order n
17178
Order of $\phi(g)$ divides the order of $g$
30676
$G'$ and the product of all the elements in an odd order group
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
114662
Construction of a specific non-commutative and infinite group (with conditions on the order of the elements)
129789
Find all Quotient (or Factor) Groups of $D_4$ (Dihedral Group of order $8$)
45770
Does the order, lattice of subgroups, and lattice of factor groups, uniquely determine a group up to isomorphism?
122970
A question on $p$-groups, and order of its commutator subgroup.