Question

The only surjective homomorphism from $S_n$ to $\{1,-1\}$ is $\text{sign}$

score 983 · Answer 1 · 2020-05-06 23:33:34

983

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The only surjective homomorphism from $S_n$ to $\{1,-1\}$ is $\text{sign}$

Published on 06 May 2020 - 23:33

score 161 · Answer 2 · 2026-03-25 07:43:52

161

Views

A special type of Gauss sum

Published on 25 Mar 2026 - 7:43

score 451 · Answer 3 · 2020-05-09 19:49:51

451

Views

Proving a continuous homomorphism from $(\mathbb{R}^2,+)$ to $(\mathbb{R}, +)$ is a linear transformation.

Published on 09 May 2020 - 19:49

score 163 · Answer 4 · 2020-05-10 12:51:47

163

Views

Number of Ring homomorphisms $\phi:\mathbb{Z}_{12}\longrightarrow\mathbb{Z}_{12}$

Published on 10 May 2020 - 12:51

score 447 · Answer 5 · 2026-03-27 23:48:17

447

Views

Dual to group algebra of a finite group as a Hopf Algebra

Published on 27 Mar 2026 - 23:48

score 45 · Answer 6 · 2020-05-17 09:48:13

45

Views

If $m \mid n$, show that there is a one-to-one homomorphism $\mathbb{Z}_m \to \mathbb{Z}_n$.

Published on 17 May 2020 - 9:48

score 104 · Answer 7 · 2020-05-17 12:30:01

104

Views

Characterizing image of group homomorphism based on group order

Published on 17 May 2020 - 12:30

score 234 · Answer 8 · 2020-05-17 15:52:20

234

Views

Determine the number of homomorphisms from $S_{3} \rightarrow \Bbb Z_{2} \times \Bbb Z_{4}$.

Published on 17 May 2020 - 15:52

score 151 · Answer 9 · 2026-03-25 23:13:08

151

Views

Show that there is an injective homomorphism from $G_2 = \langle a, b \mid aba^{-1}b^{-1}\rangle$ to $G_1 = \langle x, y \mid xyx^{-1}y\rangle$.

Published on 25 Mar 2026 - 23:13

score 279 · Answer 10 · 2026-03-26 14:22:32

279

Views

Epimorphism from free product to direct product of groups.

Published on 26 Mar 2026 - 14:22

score 255 · Answer 11 · 2026-03-26 17:47:42

255

Views

What are some nice informations about the dihedral groups,alternating groups,symmetric groups.

Published on 26 Mar 2026 - 17:47

score 44 · Answer 12 · 2020-05-19 16:27:24

44

Views

Identifying group homomorphisms

Published on 19 May 2020 - 16:27

score 120 · Answer 13 · 2026-03-25 08:09:55

120

Views

Continuity of a Group Homomorphism, Representation of SU(2)

Published on 25 Mar 2026 - 8:09

score 192 · Answer 14 · 2020-05-22 23:47:38

192

Views

Show $G\cong \ker(f) \times \mathbb{Z}$ for abelian $G$

Published on 22 May 2020 - 23:47

score 127 · Answer 15 · 2020-05-25 06:38:34

127

Views

Number of homomorphisms from direct products of $\mathbb{Z}_n$ to $\mathbb{Z}_{18}$

Published on 25 May 2020 - 6:38

List Question

The only surjective homomorphism from $S_n$ to $\{1,-1\}$ is $\text{sign}$

A special type of Gauss sum

Proving a continuous homomorphism from $(\mathbb{R}^2,+)$ to $(\mathbb{R}, +)$ is a linear transformation.

Number of Ring homomorphisms $\phi:\mathbb{Z}_{12}\longrightarrow\mathbb{Z}_{12}$

Dual to group algebra of a finite group as a Hopf Algebra

If $m \mid n$, show that there is a one-to-one homomorphism $\mathbb{Z}_m \to \mathbb{Z}_n$.

Characterizing image of group homomorphism based on group order

Determine the number of homomorphisms from $S_{3} \rightarrow \Bbb Z_{2} \times \Bbb Z_{4}$.

Show that there is an injective homomorphism from $G_2 = \langle a, b \mid aba^{-1}b^{-1}\rangle$ to $G_1 = \langle x, y \mid xyx^{-1}y\rangle$.

Epimorphism from free product to direct product of groups.

What are some nice informations about the dihedral groups,alternating groups,symmetric groups.

Identifying group homomorphisms

Continuity of a Group Homomorphism, Representation of SU(2)

Show $G\cong \ker(f) \times \mathbb{Z}$ for abelian $G$

Number of homomorphisms from direct products of $\mathbb{Z}_n$ to $\mathbb{Z}_{18}$

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