Question

Prove that sgn is a homomorphism from $S_n\to\{1,-1\}$.

score 2.1k · Answer 1 · 2017-11-01 21:52:52

2.1k

Views

Prove that sgn is a homomorphism from $S_n\to\{1,-1\}$.

Published on 01 Nov 2017 - 21:52

score 184 · Answer 2 · 2017-11-02 15:53:09

184

Views

Homomorphism and kernel of p-adic integers

Published on 02 Nov 2017 - 15:53

score 90 · Answer 3 · 2026-03-27 16:03:48

90

Views

For which $n$ does there exist a surjective homomorphism from $SL_n(\mathbf{R})\rightarrow PGL_n(\mathbf{R})$?

Published on 27 Mar 2026 - 16:03

score 400 · Answer 4 · 2017-11-03 17:20:09

400

Views

The identity element of the group of all group homomorphisms

Published on 03 Nov 2017 - 17:20

score 691 · Answer 5 · 2017-11-03 18:24:04

691

Views

No Nontrivial Homomorphism from $\Bbb{Q}$ to $S_3$?

Published on 03 Nov 2017 - 18:24

score 96 · Answer 6 · 2017-11-08 09:06:49

96

Views

Number of solutions of $x^n = 1 \pmod{p}$ for every integer $n$

Published on 08 Nov 2017 - 9:06

score 73 · Answer 7 · 2017-11-08 19:19:29

73

Views

Congruence between groups when a homomorphism is present

Published on 08 Nov 2017 - 19:19

score 33 · Answer 8 · 2026-03-30 20:44:06

33

Views

Exist an easy way to find a homomorphism from $\mathbb{Z}_3$ to $\operatorname{Aut}(K_4 \times \mathbb{Z}_2)$?

Published on 30 Mar 2026 - 20:44

score 88 · Answer 9 · 2026-02-23 08:27:01

88

Views

Number of solutions to $x^n=e$ in group G is divisible by n, where n divides o(G)

Published on 23 Feb 2026 - 8:27

score 71 · Answer 10 · 2017-11-09 14:13:49

71

Views

Kernel of homomorphism from $\mathbb{R} \to \mathbb{T} \times \mathbb{T}$

Published on 09 Nov 2017 - 14:13

score 44 · Answer 11 · 2017-11-09 14:46:49

44

Views

Show whether the function $\phi(x)=21x \bmod 36$ is one-to-one and/or onto

Published on 09 Nov 2017 - 14:46

score 132 · Answer 12 · 2017-11-10 13:25:03

132

Views

Homomorphisms of Groups

Published on 10 Nov 2017 - 13:25

score 345 · Answer 13 · 2017-11-10 19:44:06

345

Views

Homomorphism in which e is identity h(e) is not

Published on 10 Nov 2017 - 19:44

score 172 · Answer 14 · 2017-11-11 19:02:59

172

Views

Injective homomorphism from $\mathbb Z/q \mathbb Z$ to $\text{Aut}(\mathbb Z/p \mathbb Z)$

Published on 11 Nov 2017 - 19:02

score 238 · Answer 15 · 2026-03-27 20:21:07

238

Views

For any $n ≥3$ there are exactly $4$ distinct homomorphisms from $Z_2$ into $Aut(Z_2^n).$

Published on 27 Mar 2026 - 20:21

List Question

Prove that sgn is a homomorphism from $S_n\to\{1,-1\}$.

Homomorphism and kernel of p-adic integers

For which $n$ does there exist a surjective homomorphism from $SL_n(\mathbf{R})\rightarrow PGL_n(\mathbf{R})$?

The identity element of the group of all group homomorphisms

No Nontrivial Homomorphism from $\Bbb{Q}$ to $S_3$?

Number of solutions of $x^n = 1 \pmod{p}$ for every integer $n$

Congruence between groups when a homomorphism is present

Exist an easy way to find a homomorphism from $\mathbb{Z}_3$ to $\operatorname{Aut}(K_4 \times \mathbb{Z}_2)$?

Number of solutions to $x^n=e$ in group G is divisible by n, where n divides o(G)

Kernel of homomorphism from $\mathbb{R} \to \mathbb{T} \times \mathbb{T}$

Show whether the function $\phi(x)=21x \bmod 36$ is one-to-one and/or onto

Homomorphisms of Groups

Homomorphism in which e is identity h(e) is not

Injective homomorphism from $\mathbb Z/q \mathbb Z$ to $\text{Aut}(\mathbb Z/p \mathbb Z)$

For any $n ≥3$ there are exactly $4$ distinct homomorphisms from $Z_2$ into $Aut(Z_2^n).$

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