Question

Lift of a generator of a non-trivial quotient of a cyclic group with prime power order must be a generator of the whole group

score 205 · Answer 1 · 2018-11-08 15:39:13

205

Views

Lift of a generator of a non-trivial quotient of a cyclic group with prime power order must be a generator of the whole group

Published on 08 Nov 2018 - 15:39

score 1.5k · Answer 2 · 2018-11-13 11:19:14

1.5k

Views

Quotient group of $C^*$ by Circle group is isomorphic to $R^+$

Published on 13 Nov 2018 - 11:19

score 369 · Answer 3 · 2018-11-16 13:59:47

369

Views

Factor square root out of quotient

Published on 16 Nov 2018 - 13:59

score 542 · Answer 4 · 2018-11-19 00:26:12

542

Views

The order of an element in a quotient group

Published on 19 Nov 2018 - 0:26

score 89 · Answer 5 · 2018-11-19 23:30:42

89

Views

If we divide a group and a proper subgroup of this group by the same normal subgroup, can the quotients be equal?

Published on 19 Nov 2018 - 23:30

score 64 · Answer 6 · 2018-11-20 00:28:20

64

Views

General concept of 'quotient'

Published on 20 Nov 2018 - 0:28

score 64 · Answer 7 · 2018-11-21 03:06:09

64

Views

$\mathbb{F}_2[X]/(S) \cong \mathbb{F}_4 $

Published on 21 Nov 2018 - 3:06

score 2k · Answer 8 · 2018-11-23 23:15:52

2k

Views

Suppose $H$ and $K$ are normal subgroups of $G$. Prove that $G/H \times G/K$ has a subgroup that is isomorphic to $G / (H∩K)$.

Published on 23 Nov 2018 - 23:15

score 20 · Answer 9 · 2018-11-24 01:00:46

20

Views

Question concerning isomorphism of quotient groups

Published on 24 Nov 2018 - 1:00

score 55 · Answer 10 · 2018-11-25 19:37:48

55

Views

Let $G$ be a group and $H, H'$ be subgroups of $G$ where $H$ is normal. Under which circumstances is $H \cap H'$ a normal subgroup of $H$?

Published on 25 Nov 2018 - 19:37

score 518 · Answer 11 · 2018-11-29 20:49:11

518

Views

Is there a general way to calculate the fundamental group of a quotient space?

Published on 29 Nov 2018 - 20:49

score 54 · Answer 12 · 2018-12-05 02:27:04

54

Views

Quotient group as a manifold

Published on 05 Dec 2018 - 2:27

score 1.7k · Answer 13 · 2018-12-05 18:48:40

1.7k

Views

Give an example of: A group with an element A of order 3, an element B with order 4, where order of AB is less than 12

Published on 05 Dec 2018 - 18:48

score 94 · Answer 14 · 2018-12-08 17:39:25

94

Views

What is $D_{16}/ Z(D_{16})$?

Published on 08 Dec 2018 - 17:39

score 459 · Answer 15 · 2018-12-08 22:29:15

459

Views

Show that the quotient group $G/N$ contains a subgroup isomorphic to $H$.

Published on 08 Dec 2018 - 22:29

List Question

Lift of a generator of a non-trivial quotient of a cyclic group with prime power order must be a generator of the whole group

Quotient group of $C^*$ by Circle group is isomorphic to $R^+$

Factor square root out of quotient

The order of an element in a quotient group

If we divide a group and a proper subgroup of this group by the same normal subgroup, can the quotients be equal?

General concept of 'quotient'

$\mathbb{F}_2[X]/(S) \cong \mathbb{F}_4 $

Suppose $H$ and $K$ are normal subgroups of $G$. Prove that $G/H \times G/K$ has a subgroup that is isomorphic to $G / (H∩K)$.

Question concerning isomorphism of quotient groups

Let $G$ be a group and $H, H'$ be subgroups of $G$ where $H$ is normal. Under which circumstances is $H \cap H'$ a normal subgroup of $H$?

Is there a general way to calculate the fundamental group of a quotient space?

Quotient group as a manifold

Give an example of: A group with an element A of order 3, an element B with order 4, where order of AB is less than 12

What is $D_{16}/ Z(D_{16})$?

Show that the quotient group $G/N$ contains a subgroup isomorphic to $H$.

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