Question

Is there surjective homomorphism of the fundamental group $\pi_1(\mathbb{R}^3 - 6_1^2)$ onto the dihedral group $D_{2\cdot 3}$ of $6$ elements?

score 113 · Answer 1 · 2026-03-29 16:30:23

113

Views

Is there surjective homomorphism of the fundamental group $\pi_1(\mathbb{R}^3 - 6_1^2)$ onto the dihedral group $D_{2\cdot 3}$ of $6$ elements?

Published on 29 Mar 2026 - 16:30

score 312 · Answer 2 · 2022-07-28 14:54:36

312

Views

Homomorphism from unit circle to unit circle

Published on 28 Jul 2022 - 14:54

score 154 · Answer 3 · 2022-07-30 20:16:37

154

Views

Let $G$ be a group, $H < G$, and $A_H=\{g\mid\bar{g}\subset H\}$ where $\bar{g}$ is the conjugacy class of $g$. Prove $A_H\lhd G$.

Published on 30 Jul 2022 - 20:16

score 100 · Answer 4 · 2026-04-02 01:00:26

100

Views

Finding all group homomorphisms $\varphi:\mathbb{Z}/4\mathbb{Z} \to \text{Aut}(\mathbb{Z}/5\mathbb{Z})$

Published on 02 Apr 2026 - 1:00

score 65 · Answer 5 · 2026-03-27 04:56:54

65

Views

Find an homomorphism $\phi:\mathbb{Z}^4 \to G$

Published on 27 Mar 2026 - 4:56

score 61 · Answer 6 · 2022-08-02 09:25:17

61

Views

How to see isomorphisms fast

Published on 02 Aug 2022 - 9:25

score 36 · Answer 7 · 2026-03-29 15:33:20

36

Views

Normality of $\frac{G_{i}\cap N}{G_{i+1}\cap N}$ in $\frac{G_i}{G_{i+1}}$ related to a composition series

Published on 29 Mar 2026 - 15:33

score 34 · Answer 8 · 2026-03-27 02:39:22

34

Views

$\phi$-torsion of a group

Published on 27 Mar 2026 - 2:39

score 57 · Answer 9 · 2022-08-08 11:57:07

57

Views

If $H$ is a subgroup of $G$, then the homomorphism $i: HN/N \to p(H)$, defined by $i(xN) = p(x)$ is a topological isomorphism

Published on 08 Aug 2022 - 11:57

score 110 · Answer 10 · 2026-02-23 18:48:31

110

Views

Does a free group $F$ of finite rank $n$ have finitely many retracts (as a subgroup)?

Published on 23 Feb 2026 - 18:48

score 75 · Answer 11 · 2022-08-12 11:45:09

75

Views

First Isomorphism Theorem: Does each homomorphism has to be surjective? Is it possible to define an homomorphism $\phi:G\to H$ such that $|G|<|H|$?

Published on 12 Aug 2022 - 11:45

score 109 · Answer 12 · 2022-08-13 21:19:57

109

Views

Does there exist a group homomorphism $(\mathbb{Q}_p, +) \to (\mathbb{R}, +)$?

Published on 13 Aug 2022 - 21:19

score 165 · Answer 13 · 2026-03-29 16:28:14

165

Views

Extended Homomorphism from $D_{2n}$ to $GL_2(\mathbb{R})$

Published on 29 Mar 2026 - 16:28

score 144 · Answer 14 · 2026-03-29 16:55:58

144

Views

Constructing homomorphism from a group to its normal subgroups

Published on 29 Mar 2026 - 16:55

score 52 · Answer 15 · 2022-08-24 21:30:25

52

Views

If $f:G \to H$ is an injective homomorphism of groups and $a \in G$, prove that $\vert f(a) \vert = \vert a \vert$.

Published on 24 Aug 2022 - 21:30

List Question

Is there surjective homomorphism of the fundamental group $\pi_1(\mathbb{R}^3 - 6_1^2)$ onto the dihedral group $D_{2\cdot 3}$ of $6$ elements?

Homomorphism from unit circle to unit circle

Let $G$ be a group, $H < G$, and $A_H=\{g\mid\bar{g}\subset H\}$ where $\bar{g}$ is the conjugacy class of $g$. Prove $A_H\lhd G$.

Finding all group homomorphisms $\varphi:\mathbb{Z}/4\mathbb{Z} \to \text{Aut}(\mathbb{Z}/5\mathbb{Z})$

Find an homomorphism $\phi:\mathbb{Z}^4 \to G$

How to see isomorphisms fast

Normality of $\frac{G_{i}\cap N}{G_{i+1}\cap N}$ in $\frac{G_i}{G_{i+1}}$ related to a composition series

$\phi$-torsion of a group

If $H$ is a subgroup of $G$, then the homomorphism $i: HN/N \to p(H)$, defined by $i(xN) = p(x)$ is a topological isomorphism

Does a free group $F$ of finite rank $n$ have finitely many retracts (as a subgroup)?

First Isomorphism Theorem: Does each homomorphism has to be surjective? Is it possible to define an homomorphism $\phi:G\to H$ such that $|G|<|H|$?

Does there exist a group homomorphism $(\mathbb{Q}_p, +) \to (\mathbb{R}, +)$?

Extended Homomorphism from $D_{2n}$ to $GL_2(\mathbb{R})$

Constructing homomorphism from a group to its normal subgroups

If $f:G \to H$ is an injective homomorphism of groups and $a \in G$, prove that $\vert f(a) \vert = \vert a \vert$.

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