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 208 · Answer 1 · 2026-04-11 02:58:33

208

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 11 Apr 2026 - 2:58

score 1.5k · Answer 2 · 2026-04-10 20:01:50

1.5k

Views

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

Published on 10 Apr 2026 - 20:01

score 373 · Answer 3 · 2026-04-13 09:41:04

373

Views

Factor square root out of quotient

Published on 13 Apr 2026 - 9:41

score 545 · Answer 4 · 2026-04-14 03:46:41

545

Views

The order of an element in a quotient group

Published on 14 Apr 2026 - 3:46

score 92 · Answer 5 · 2026-04-14 19:21:55

92

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 14 Apr 2026 - 19:21

score 71 · Answer 6 · 2026-04-30 13:04:10

71

Views

General concept of 'quotient'

Published on 30 Apr 2026 - 13:04

score 67 · Answer 7 · 2026-04-16 17:02:35

67

Views

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

Published on 16 Apr 2026 - 17:02

score 2k · Answer 8 · 2026-04-14 02:13:24

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 14 Apr 2026 - 2:13

score 23 · Answer 9 · 2026-04-13 22:34:01

23

Views

Question concerning isomorphism of quotient groups

Published on 13 Apr 2026 - 22:34

score 58 · Answer 10 · 2026-04-12 05:44:58

58

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 12 Apr 2026 - 5:44

score 522 · Answer 11 · 2026-04-17 02:26:35

522

Views

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

Published on 17 Apr 2026 - 2:26

score 58 · Answer 12 · 2026-04-13 03:29:41

58

Views

Quotient group as a manifold

Published on 13 Apr 2026 - 3:29

score 1.7k · Answer 13 · 2026-04-16 03:54:29

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 16 Apr 2026 - 3:54

score 99 · Answer 14 · 2026-05-10 15:22:58

99

Views

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

Published on 10 May 2026 - 15:22

score 462 · Answer 15 · 2026-04-15 10:56:51

462

Views

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

Published on 15 Apr 2026 - 10:56

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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