Question

Find the largest possible order of an element of $\frac{\Bbb{Z}_{12}\times\Bbb{Z}_3\times\Bbb{Z}_6}{\left<(8,2,4)\right>}.$

score 70 · Answer 1 · 2020-06-07 16:56:56

70

Views

Find the largest possible order of an element of $\frac{\Bbb{Z}_{12}\times\Bbb{Z}_3\times\Bbb{Z}_6}{\left<(8,2,4)\right>}.$

Published on 07 Jun 2020 - 16:56

score 802 · Answer 2 · 2020-06-09 09:05:00

802

Views

Let $N$ be a normal subgroup of $G$ and $H$ be a subgroup of $G$ such that $ H N =G$. Prove that $H$ is a system of representatives of $N$ in $G$.

Published on 09 Jun 2020 - 9:05

score 92 · Answer 3 · 2020-06-11 00:38:25

92

Views

If $|A|=pq$ and $A\lhd B$ is a Nontrivial Normal Subgroup, the Quotient Group $A/B$ is Cyclic

Published on 11 Jun 2020 - 0:38

score 55 · Answer 4 · 2020-06-12 16:45:51

55

Views

Structure of $A_4/H$

Published on 12 Jun 2020 - 16:45

score 59 · Answer 5 · 2020-06-15 04:32:14

59

Views

Usefulness of a theorem involving quotient groups

Published on 15 Jun 2020 - 4:32

score 105 · Answer 6 · 2020-06-17 13:04:46

105

Views

If $H$ and $K$ are normal subgroups of $G$ and $G/H \cong K$, does this imply that $G/K \cong H$?

Published on 17 Jun 2020 - 13:04

score 57 · Answer 7 · 2020-06-18 12:11:51

57

Views

Quotient of $\mathbb R^n\rtimes O\left(n\right)$ by $\mathbb Z^n\rtimes D_8$

Published on 18 Jun 2020 - 12:11

score 53 · Answer 8 · 2020-06-18 14:37:55

53

Views

What is the Meaning of $Q[u_1] \cong Q[x]/\langle f(x)\rangle$?

Published on 18 Jun 2020 - 14:37

score 59 · Answer 9 · 2020-06-18 14:48:50

59

Views

Difference between 2 Quotient Rings

Published on 18 Jun 2020 - 14:48

score 1.5k · Answer 10 · 2020-06-23 19:37:44

1.5k

Views

Let $H\triangleleft G$. Prove that $G/H$ is abelian iff $ [G, G] \subseteq H$

Published on 23 Jun 2020 - 19:37

score 459 · Answer 11 · 2020-06-25 11:05:50

459

Views

The quotient of a quotient group by another quotient group

Published on 25 Jun 2020 - 11:05

score 88 · Answer 12 · 2020-06-26 16:58:17

88

Views

Quotient group isomorphic to $\mathbb Q^∗$

Published on 26 Jun 2020 - 16:58

score 54 · Answer 13 · 2020-06-26 18:25:54

54

Views

Identifying Abelian group

Published on 26 Jun 2020 - 18:25

score 69 · Answer 14 · 2020-07-03 12:15:22

69

Views

Describe $\mathbb{Z} \times \mathbb{Z} /\mathbb{3Z}\times\mathbb{Z} $

Published on 03 Jul 2020 - 12:15

score 44 · Answer 15 · 2020-07-05 16:42:27

44

Views

What is the set of units in $ (\mathbb Z/n \mathbb Z)$ equal to $\{k+n \mathbb Z : gcd(n,k)=1\} $

Published on 05 Jul 2020 - 16:42

List Question

Find the largest possible order of an element of $\frac{\Bbb{Z}_{12}\times\Bbb{Z}_3\times\Bbb{Z}_6}{\left<(8,2,4)\right>}.$

Let $N$ be a normal subgroup of $G$ and $H$ be a subgroup of $G$ such that $ H N =G$. Prove that $H$ is a system of representatives of $N$ in $G$.

If $|A|=pq$ and $A\lhd B$ is a Nontrivial Normal Subgroup, the Quotient Group $A/B$ is Cyclic

Structure of $A_4/H$

Usefulness of a theorem involving quotient groups

If $H$ and $K$ are normal subgroups of $G$ and $G/H \cong K$, does this imply that $G/K \cong H$?

Quotient of $\mathbb R^n\rtimes O\left(n\right)$ by $\mathbb Z^n\rtimes D_8$

What is the Meaning of $Q[u_1] \cong Q[x]/\langle f(x)\rangle$?

Difference between 2 Quotient Rings

Let $H\triangleleft G$. Prove that $G/H$ is abelian iff $ [G, G] \subseteq H$

The quotient of a quotient group by another quotient group

Quotient group isomorphic to $\mathbb Q^∗$

Identifying Abelian group

Describe $\mathbb{Z} \times \mathbb{Z} /\mathbb{3Z}\times\mathbb{Z} $

What is the set of units in $ (\mathbb Z/n \mathbb Z)$ equal to $\{k+n \mathbb Z : gcd(n,k)=1\} $

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