Question

Definition of a quotient group in Dummit-Foote

score 214 · Answer 1 · 2026-03-21 18:14:03

214

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Definition of a quotient group in Dummit-Foote

Published on 21 Mar 2026 - 18:14

score 880 · Answer 2 · 2018-10-06 07:12:21

880

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Why is $\mathbb{Q}/ \mathbb{Z}$ called the groups of rationals modulo one?

Published on 06 Oct 2018 - 7:12

score 441 · Answer 3 · 2018-10-07 18:17:02

441

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If $H\subseteq G$ is a cocompact subgroup, then $G=KH$ for $K\subseteq G$ compact subgroup

Published on 07 Oct 2018 - 18:17

score 242 · Answer 4 · 2026-03-25 06:04:29

242

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Find number of invertible elements in $\mathbb{Z}[i]/(220+55i)\mathbb{Z}[i]$

Published on 25 Mar 2026 - 6:04

score 493 · Answer 5 · 2018-10-15 10:59:13

493

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Let $P$ be a partition of a group with $AB \subseteq C$. Why is $1 \in P_n$? $P_n$ is the equivalence class of $n \in N$ and $1 \in N=P_1$.

Published on 15 Oct 2018 - 10:59

score 737 · Answer 6 · 2018-10-15 11:35:08

737

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If S is a normal subgroup, identify the quotient group G/S. What are the $\varphi(G)$'s?

Published on 15 Oct 2018 - 11:35

score 2.1k · Answer 7 · 2018-10-15 12:36:39

2.1k

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Write down all the elements of the quotient group $Z_{18} / \langle 6\rangle$. Is any element of order $5?$ Give reasons for your answer.

Published on 15 Oct 2018 - 12:36

score 78 · Answer 8 · 2018-10-15 16:23:23

78

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Construction of a Finite Abelian Group

Published on 15 Oct 2018 - 16:23

score 29 · Answer 9 · 2018-10-15 19:33:24

29

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How do I write $\Bbb Z{\left[\frac16\right]}\cap\left[\frac23,\frac43\right),+$ modulo $\frac23$?

Published on 15 Oct 2018 - 19:33

score 47 · Answer 10 · 2018-10-21 18:02:11

47

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Let $K \subseteq G$. Nec. and suff. cond. for that $\exists$ a normal subgr $H$ of $G$ s.t $exists$ transversal $I$ s.t $I \subseteq K$.

Published on 21 Oct 2018 - 18:02

score 100 · Answer 11 · 2018-10-21 18:04:00

100

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Intuitive explanation for: let $I_G$ be the group of > all inner automorphisms of $G$. Then $I_g$ is isomorphic to $G/C_G$

Published on 21 Oct 2018 - 18:04

score 55 · Answer 12 · 2018-10-31 21:57:34

55

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Are two lifts of a generator of a cyclic quotient conjugated?

Published on 31 Oct 2018 - 21:57

score 4.6k · Answer 13 · 2018-11-05 00:21:41

4.6k

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$GL(2,R) / SL(2,R)$ isomorphic to R*

Published on 05 Nov 2018 - 0:21

score 154 · Answer 14 · 2018-11-05 05:57:08

154

Views

Given that $G$ is cyclic then $G/N$ is cyclic.

Published on 05 Nov 2018 - 5:57

score 156 · Answer 15 · 2018-11-08 11:35:22

156

Views

Multiplicative quotient - what's the correct notation? Does a quotient group contain singletons or cosets?

Published on 08 Nov 2018 - 11:35

List Question

Definition of a quotient group in Dummit-Foote

Why is $\mathbb{Q}/ \mathbb{Z}$ called the groups of rationals modulo one?

If $H\subseteq G$ is a cocompact subgroup, then $G=KH$ for $K\subseteq G$ compact subgroup

Find number of invertible elements in $\mathbb{Z}[i]/(220+55i)\mathbb{Z}[i]$

Let $P$ be a partition of a group with $AB \subseteq C$. Why is $1 \in P_n$? $P_n$ is the equivalence class of $n \in N$ and $1 \in N=P_1$.

If S is a normal subgroup, identify the quotient group G/S. What are the $\varphi(G)$'s?

Write down all the elements of the quotient group $Z_{18} / \langle 6\rangle$. Is any element of order $5?$ Give reasons for your answer.

Construction of a Finite Abelian Group

How do I write $\Bbb Z{\left[\frac16\right]}\cap\left[\frac23,\frac43\right),+$ modulo $\frac23$?

Let $K \subseteq G$. Nec. and suff. cond. for that $\exists$ a normal subgr $H$ of $G$ s.t $exists$ transversal $I$ s.t $I \subseteq K$.

Intuitive explanation for: let $I_G$ be the group of > all inner automorphisms of $G$. Then $I_g$ is isomorphic to $G/C_G$

Are two lifts of a generator of a cyclic quotient conjugated?

$GL(2,R) / SL(2,R)$ isomorphic to R*

Given that $G$ is cyclic then $G/N$ is cyclic.

Multiplicative quotient - what's the correct notation? Does a quotient group contain singletons or cosets?

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