Question

Circulant Matrices and Ring of Polinomials

score 92 · Answer 1 · 2026-03-25 03:22:54

92

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Circulant Matrices and Ring of Polinomials

Published on 25 Mar 2026 - 3:22

score 831 · Answer 2 · 2026-03-26 14:34:49

831

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In proving G contains an element of order 15 if contains normal subgroups of orders 3 and 5, respectively, is $HK$ itself cyclic with order 15?

Published on 26 Mar 2026 - 14:34

score 738 · Answer 3 · 2026-03-25 11:15:53

738

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

Published on 25 Mar 2026 - 11:15

score 1.5k · Answer 4 · 2026-03-27 03:00:03

1.5k

Views

What are the isomorphisms from $\mathbb{Z}$ to itself?

Published on 27 Mar 2026 - 3:00

score 859 · Answer 5 · 2018-10-19 23:56:24

859

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Detail in bijection between Inn(G) and G/Z(G)?

Published on 19 Oct 2018 - 23:56

score 3.9k · Answer 6 · 2026-03-26 13:02:41

3.9k

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If $H$ and $K$ are normal subgroups of $G$ and $H\bigcap K = \{e\}$, prove that $G$ is isomorphic to a subgroup of $G/H \times G/K$

Published on 26 Mar 2026 - 13:02

score 101 · Answer 7 · 2026-03-25 12:50:57

101

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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 25 Mar 2026 - 12:50

score 272 · Answer 8 · 2026-03-25 03:24:15

272

Views

Show linear mapping is isomorphism

Published on 25 Mar 2026 - 3:24

score 61 · Answer 9 · 2026-03-25 03:02:53

61

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Consider the set F under the operation of composition of functions ◦.

Published on 25 Mar 2026 - 3:02

score 1.1k · Answer 10 · 2026-03-25 09:28:25

1.1k

Views

A 2-Sylow subgroup of $S_5$ is isomorphic to $D_4$

Published on 25 Mar 2026 - 9:28

score 119 · Answer 11 · 2026-03-28 02:22:23

119

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Confused about coverings for Lie groups

Published on 28 Mar 2026 - 2:22

score 888 · Answer 12 · 2026-03-28 20:11:40

888

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Two non abelian groups of order pq are isomorphic

Published on 28 Mar 2026 - 20:11

score 1.4k · Answer 13 · 2026-03-25 15:52:43

1.4k

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Let $\phi:\Bbb{Z}_{20} \to \Bbb{Z}_{20}$ be an automorphism and $\phi(5)=5$. What are the possibilities of $\phi(x)$?

Published on 25 Mar 2026 - 15:52

score 115 · Answer 14 · 2026-03-26 04:14:45

115

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Show that a subgroup of order $N \in \mathbb{N}$ is isomorphic to $\mathbb{Z}/n\mathbb{Z} × \mathbb{Z}/nn'\mathbb{Z}$.

Published on 26 Mar 2026 - 4:14

score 301 · Answer 15 · 2026-03-27 00:06:39

301

Views

What is wrong with the followig proof that $\mathbb{Z}$ is isomorphic to $\mathbb{Z} \times \mathbb{Z}$

Published on 27 Mar 2026 - 0:06

List Question

Circulant Matrices and Ring of Polinomials

In proving G contains an element of order 15 if contains normal subgroups of orders 3 and 5, respectively, is $HK$ itself cyclic with order 15?

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

What are the isomorphisms from $\mathbb{Z}$ to itself?

Detail in bijection between Inn(G) and G/Z(G)?

If $H$ and $K$ are normal subgroups of $G$ and $H\bigcap K = \{e\}$, prove that $G$ is isomorphic to a subgroup of $G/H \times G/K$

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

Show linear mapping is isomorphism

Consider the set F under the operation of composition of functions ◦.

A 2-Sylow subgroup of $S_5$ is isomorphic to $D_4$

Confused about coverings for Lie groups

Two non abelian groups of order pq are isomorphic

Let $\phi:\Bbb{Z}_{20} \to \Bbb{Z}_{20}$ be an automorphism and $\phi(5)=5$. What are the possibilities of $\phi(x)$?

Show that a subgroup of order $N \in \mathbb{N}$ is isomorphic to $\mathbb{Z}/n\mathbb{Z} × \mathbb{Z}/nn'\mathbb{Z}$.

What is wrong with the followig proof that $\mathbb{Z}$ is isomorphic to $\mathbb{Z} \times \mathbb{Z}$

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