Question

If there exists an element $x$ of order $n$ in $G'$, then we must have an element of order $n$ in $G$?

score 52 · Answer 1 · 2019-01-25 04:34:06

52

Views

If there exists an element $x$ of order $n$ in $G'$, then we must have an element of order $n$ in $G$?

Published on 25 Jan 2019 - 4:34

score 66 · Answer 2 · 2019-01-25 15:14:10

66

Views

Homomorphism of groups, subgroups

Published on 25 Jan 2019 - 15:14

score 213 · Answer 3 · 2026-03-25 14:25:50

213

Views

Kernel of $G\ast H\to G\times H$ is free

Published on 25 Mar 2026 - 14:25

score 48 · Answer 4 · 2019-01-28 13:20:57

48

Views

Let G be a group. Prove that the function: $G→G, x→x^2$ is a group homomorphism if and only if G is an abelian group.

Published on 28 Jan 2019 - 13:20

score 110 · Answer 5 · 2019-01-30 16:43:44

110

Views

Homomorphism $f: \mathbb{Z}_{12} \longrightarrow \mathbb{Z}_{30}$

Published on 30 Jan 2019 - 16:43

score 453 · Answer 6 · 2026-03-26 09:45:01

453

Views

Do isomorphic groups share a binary operation?

Published on 26 Mar 2026 - 9:45

score 676 · Answer 7 · 2019-02-01 15:44:49

676

Views

Show that $f^{-1}\{f(a)\}=a\text{Ker}f$

Published on 01 Feb 2019 - 15:44

score 78 · Answer 8 · 2019-02-02 15:07:05

78

Views

How do the elements of the set $(\mathbb{Q}\backslash\{0\},\cdot)/(\mathbb{Q}^{+},\cdot)$ look like?

Published on 02 Feb 2019 - 15:07

score 597 · Answer 9 · 2019-02-02 17:27:59

597

Views

Excercise with the normal subgroup $K$ of $G$ with $K:=\bigcap\{H \text{ subgroup of } G: \forall_{x,y\in G}:xyx^{-1}y^{-1}\in H\}$

Published on 02 Feb 2019 - 17:27

score 70 · Answer 10 · 2026-03-25 14:37:59

70

Views

Elementary question about well-definedness of induced homomorphism

Published on 25 Mar 2026 - 14:37

score 123 · Answer 11 · 2026-03-25 22:30:09

123

Views

Show that $Ax=0$.

Published on 25 Mar 2026 - 22:30

score 54 · Answer 12 · 2019-02-07 16:10:00

54

Views

Are $\mathbb{Z}$ and $\mathbb{Z}_n$ the only rings (with identity) whose modules are equivalent to abelian groups?

Published on 07 Feb 2019 - 16:10

score 88 · Answer 13 · 2019-02-07 22:09:20

Show that a function from $\Bbb Z / 3600\mathbb{Z}$ to $\mathbb{Z} / 1200\mathbb{Z}$ is a well defined group homomorphism of additive groups

score 439 · Answer 14 · 2019-02-08 01:39:13

439

Views

Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.

Published on 08 Feb 2019 - 1:39

score 1k · Answer 15 · 2019-02-08 18:55:53

1k

Views

Hatcher Exercise 3.2.9

Published on 08 Feb 2019 - 18:55

List Question

If there exists an element $x$ of order $n$ in $G'$, then we must have an element of order $n$ in $G$?

Homomorphism of groups, subgroups

Kernel of $G\ast H\to G\times H$ is free

Let G be a group. Prove that the function: $G→G, x→x^2$ is a group homomorphism if and only if G is an abelian group.

Homomorphism $f: \mathbb{Z}_{12} \longrightarrow \mathbb{Z}_{30}$

Do isomorphic groups share a binary operation?

Show that $f^{-1}\{f(a)\}=a\text{Ker}f$

How do the elements of the set $(\mathbb{Q}\backslash\{0\},\cdot)/(\mathbb{Q}^{+},\cdot)$ look like?

Excercise with the normal subgroup $K$ of $G$ with $K:=\bigcap\{H \text{ subgroup of } G: \forall_{x,y\in G}:xyx^{-1}y^{-1}\in H\}$

Elementary question about well-definedness of induced homomorphism

Show that $Ax=0$.

Are $\mathbb{Z}$ and $\mathbb{Z}_n$ the only rings (with identity) whose modules are equivalent to abelian groups?

Show that a function from $\Bbb Z / 3600\mathbb{Z}$ to $\mathbb{Z} / 1200\mathbb{Z}$ is a well defined group homomorphism of additive groups

Let $f : G → G_1$ be a surjective homomorphism (also called epimorphism) from $G$ to another group $G_1$. Prove that $f(Z(G)) \subseteq Z(G_1)$.

Hatcher Exercise 3.2.9

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