Question

Describe two different isomorphisms between U(20) and U(16)

score 158 · Answer 1 · 2021-11-09 14:27:06

158

Views

Describe two different isomorphisms between U(20) and U(16)

Published on 09 Nov 2021 - 14:27

score 55 · Answer 2 · 2026-04-06 14:41:45

55

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Let $G$ and $H$ be groups and $\varphi:G \to H$ a group isomorphism. Show that if $H$ is cyclic, then $G$ is cyclic also.

Published on 06 Apr 2026 - 14:41

score 244 · Answer 3 · 2026-03-27 04:17:45

244

Views

Category theoretical proof that Abelianization commutes with products of group

Published on 27 Mar 2026 - 4:17

score 99 · Answer 4 · 2026-04-06 14:38:09

99

Views

An isomorphism between $U(13)$ and $\mathbb{Z}_3 \times \mathbb{Z}_4$

Published on 06 Apr 2026 - 14:38

score 286 · Answer 5 · 2026-03-28 02:06:40

286

Views

Find the number of homomorphisms from $A_4\to\mathbb Z_3$ and $A_4\to S_3$?

Published on 28 Mar 2026 - 2:06

score 180 · Answer 6 · 2026-04-01 13:43:38

180

Views

Let $C_n$ be a cyclic group of order $n$. Find all automorphisms of $C_n$.

Published on 01 Apr 2026 - 13:43

score 107 · Answer 7 · 2026-04-01 08:01:40

107

Views

How to prove that normal subgroups are mapped to congruences?

Published on 01 Apr 2026 - 8:01

score 78 · Answer 8 · 2026-03-28 16:25:53

78

Views

How to prove $ \Phi:H_{1}\times...\times H_{n}\to G $ defined by $ \Phi\left(h_{1},...,h_{n}\right):=h_{1}\cdot...\cdot h_{n} $ is an isomorphism

Published on 28 Mar 2026 - 16:25

score 144 · Answer 9 · 2026-03-30 13:57:33

144

Views

Countability of Gal(C/Q) and isomorphism of its subgroups

Published on 30 Mar 2026 - 13:57

score 1.4k · Answer 10 · 2021-11-22 02:15:42

1.4k

Views

Prove that $\mathbb{Q}[\sqrt{2}]=a+b\sqrt{2}$ is isomorphic to $\mathbb{Q}[x]/(x^2-2)$.

Published on 22 Nov 2021 - 2:15

score 35 · Answer 11 · 2026-03-26 03:12:30

35

Views

Isomorphism of enveloping algebra homomorphisms to $k$-homomorphisms?

Published on 26 Mar 2026 - 3:12

score 252 · Answer 12 · 2021-11-26 21:05:32

252

Views

Prove $A$, the set of all complex numbers with modulus $1$, is a subgroup of $\Bbb C^$. Prove also that $\Bbb C^\cong\Bbb R^+\times A$.

Published on 26 Nov 2021 - 21:05

score 56 · Answer 13 · 2026-04-08 04:10:44

56

Views

Why choose $ab$ and $ab^2$ for group with $6$ elements?

Published on 08 Apr 2026 - 4:10

score 47 · Answer 14 · 2021-11-28 22:30:41

47

Views

Is correct to say $H\times K$ is a subgroup of $G$ and its order is $q$?

Published on 28 Nov 2021 - 22:30

score 98 · Answer 15 · 2026-03-26 16:05:46

98

Views

Order 12 group with 3 generators, can I reduce to 2 generators?

Published on 26 Mar 2026 - 16:05

List Question

Describe two different isomorphisms between U(20) and U(16)

Let $G$ and $H$ be groups and $\varphi:G \to H$ a group isomorphism. Show that if $H$ is cyclic, then $G$ is cyclic also.

Category theoretical proof that Abelianization commutes with products of group

An isomorphism between $U(13)$ and $\mathbb{Z}_3 \times \mathbb{Z}_4$

Find the number of homomorphisms from $A_4\to\mathbb Z_3$ and $A_4\to S_3$?

Let $C_n$ be a cyclic group of order $n$. Find all automorphisms of $C_n$.

How to prove that normal subgroups are mapped to congruences?

How to prove $ \Phi:H_{1}\times...\times H_{n}\to G $ defined by $ \Phi\left(h_{1},...,h_{n}\right):=h_{1}\cdot...\cdot h_{n} $ is an isomorphism

Countability of Gal(C/Q) and isomorphism of its subgroups

Prove that $\mathbb{Q}[\sqrt{2}]=a+b\sqrt{2}$ is isomorphic to $\mathbb{Q}[x]/(x^2-2)$.

Isomorphism of enveloping algebra homomorphisms to $k$-homomorphisms?

Prove $A$, the set of all complex numbers with modulus $1$, is a subgroup of $\Bbb C^$. Prove also that $\Bbb C^\cong\Bbb R^+\times A$.

Why choose $ab$ and $ab^2$ for group with $6$ elements?

Is correct to say $H\times K$ is a subgroup of $G$ and its order is $q$?

Order 12 group with 3 generators, can I reduce to 2 generators?

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