Question

M an R-module, where M is a commutative ring, if $M≅R/I$ for some ideal I of R, then $M$ is a cyclic R-module

score 438 · Answer 1 · 2015-02-23 11:50:55

438

Views

M an R-module, where M is a commutative ring, if $M≅R/I$ for some ideal I of R, then $M$ is a cyclic R-module

Published on 23 Feb 2015 - 11:50

score 290 · Answer 2 · 2015-02-25 22:18:24

290

Views

In a group of order $pq^2$, if p divides $|Z(G)|$, then G is abelian

Published on 25 Feb 2015 - 22:18

score 800 · Answer 3 · 2015-02-26 01:40:27

800

Views

$G$ is a commutative group of order 72, which is a product of cyclic groups. What is max order of element?

Published on 26 Feb 2015 - 1:40

score 160 · Answer 4 · 2015-03-01 18:08:50

160

Views

Given a group is finite and non-abelian, why is the left coset with the centre of the group non-cyclic?

Published on 01 Mar 2015 - 18:08

score 1.9k · Answer 5 · 2015-03-01 21:43:41

1.9k

Views

Suppose $G$ is a group with $|G|=35$. Prove that if $H$ is a subgroup of $G$ with order 7, then $H$ is a normal subgroup of $G.$

Published on 01 Mar 2015 - 21:43

score 89 · Answer 6 · 2015-03-04 13:17:45

89

Views

List the elements of the cyclic subgroup $<(13, 3)>$ in $\mathbb Z_{26}$ x $\mathbb Z_{9}$

Published on 04 Mar 2015 - 13:17

score 78 · Answer 7 · 2015-03-04 17:16:13

78

Views

suppose that $G$ is a finite group and $H$ is a subgroup of $G$ that is not cyclic,I want to prove that all conjugates of $H$ are not cyclic.

Published on 04 Mar 2015 - 17:16

score 1.5k · Answer 8 · 2026-03-27 04:17:03

1.5k

Views

Showing two groups are not isomorphic using the order of their elements.

Published on 27 Mar 2026 - 4:17

score 1.6k · Answer 9 · 2015-03-05 23:10:07

1.6k

Views

Compute cycle notation

Published on 05 Mar 2015 - 23:10

score 437 · Answer 10 · 2015-03-06 01:02:57

437

Views

Express the following permutations as products of transpositions and identify them as even or odd.

Published on 06 Mar 2015 - 1:02

score 141 · Answer 11 · 2015-03-06 06:11:52

141

Views

Clarification on Lagrange's Theorem and the group $Z_n$ of integers modulo $n$

Published on 06 Mar 2015 - 6:11

score 1.5k · Answer 12 · 2015-03-06 08:27:20

1.5k

Views

How to find all ring homomorphisms from $\mathbb Z_{12} \to \mathbb Z_{30}$?

Published on 06 Mar 2015 - 8:27

score 1.2k · Answer 13 · 2015-03-06 10:31:54

1.2k

Views

A well defined homomorphism from $\mathbb{Z}/48\mathbb{Z}$ into $\mathbb{Z}/{36}$

Published on 06 Mar 2015 - 10:31

score 3.1k · Answer 14 · 2015-03-06 23:06:52

3.1k

Views

Prove that group $\mathbb{Q}\times Z_2$ is not isomorphic to $\mathbb{Q}$

Published on 06 Mar 2015 - 23:06

score 1k · Answer 15 · 2015-03-06 23:40:45

1k

Views

Show that $(\mathbb{Z}/2^n \mathbb{Z})^{\times}$ is not cyclic for any $n > 3.$

Published on 06 Mar 2015 - 23:40

List Question

M an R-module, where M is a commutative ring, if $M≅R/I$ for some ideal I of R, then $M$ is a cyclic R-module

In a group of order $pq^2$, if p divides $|Z(G)|$, then G is abelian

$G$ is a commutative group of order 72, which is a product of cyclic groups. What is max order of element?

Given a group is finite and non-abelian, why is the left coset with the centre of the group non-cyclic?

Suppose $G$ is a group with $|G|=35$. Prove that if $H$ is a subgroup of $G$ with order 7, then $H$ is a normal subgroup of $G.$

List the elements of the cyclic subgroup $<(13, 3)>$ in $\mathbb Z_{26}$ x $\mathbb Z_{9}$

suppose that $G$ is a finite group and $H$ is a subgroup of $G$ that is not cyclic,I want to prove that all conjugates of $H$ are not cyclic.

Showing two groups are not isomorphic using the order of their elements.

Compute cycle notation

Express the following permutations as products of transpositions and identify them as even or odd.

Clarification on Lagrange's Theorem and the group $Z_n$ of integers modulo $n$

How to find all ring homomorphisms from $\mathbb Z_{12} \to \mathbb Z_{30}$?

A well defined homomorphism from $\mathbb{Z}/48\mathbb{Z}$ into $\mathbb{Z}/{36}$

Prove that group $\mathbb{Q}\times Z_2$ is not isomorphic to $\mathbb{Q}$

Show that $(\mathbb{Z}/2^n \mathbb{Z})^{\times}$ is not cyclic for any $n > 3.$

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