Question

(When) is this homomorphism an isomorphism?

score 95 · Answer 1 · 2020-07-18 14:16:23

95

Views

(When) is this homomorphism an isomorphism?

Published on 18 Jul 2020 - 14:16

score 103 · Answer 2 · 2020-07-18 15:46:17

103

Views

A doubt about Proposition $27$ in textbook Algebra by Saunders MacLane and Garrett Birkhoff

Published on 18 Jul 2020 - 15:46

score 224 · Answer 3 · 2020-07-18 21:48:36

224

Views

Any morphism $\phi:G \rightarrow A$ to an abelian group $A$ factors uniquely through the projection $G \rightarrow G /[G,G]$.

Published on 18 Jul 2020 - 21:48

score 64 · Answer 4 · 2020-07-19 16:51:29

64

Views

Prove that $\phi: G / F \rightarrow \operatorname{Sym}(X)$ is a monomorphism

Published on 19 Jul 2020 - 16:51

score 115 · Answer 5 · 2026-03-25 22:30:57

115

Views

Homomorphic Image of ideal in Lie algebras

Published on 25 Mar 2026 - 22:30

score 593 · Answer 6 · 2026-03-28 11:03:33

593

Views

A simple proof of Sylow theorem for abelian groups

Published on 28 Mar 2026 - 11:03

score 120 · Answer 7 · 2026-03-26 19:18:42

120

Views

Question about the definition of tensor product of homomorphisms

Published on 26 Mar 2026 - 19:18

score 130 · Answer 8 · 2020-07-23 19:58:31

130

Views

Let $\varphi: G\rightarrow G'$ be a homomorphism. Show that for each $a \in G$, $| \varphi (a) | \le | a |$.

Published on 23 Jul 2020 - 19:58

score 111 · Answer 9 · 2020-07-26 12:27:23

111

Views

Sgn is a homomorphism of $S_n$ onto $\mu_2(Q)$ - proof

Published on 26 Jul 2020 - 12:27

score 562 · Answer 10 · 2026-03-26 21:12:42

562

Views

Describing homomorphisms from $\Bbb Z_n$ to $D_m$.

Published on 26 Mar 2026 - 21:12

score 219 · Answer 11 · 2026-03-26 14:30:24

219

Views

Prove that $\Bbb Q$ is an injective object in $\Bbb Z\text{-mod}$ using the following definition.

Published on 26 Mar 2026 - 14:30

score 78 · Answer 12 · 2020-07-28 18:53:58

78

Views

Homomorphism from $\mathbb{Z}_{120}$ to $\mathbb{Z}_{167}$

Published on 28 Jul 2020 - 18:53

score 390 · Answer 13 · 2020-07-28 23:02:16

390

Views

For groups $G,\bar{G},H$; $H$ abelian; and $\phi:G\to\bar{G}$, a homomorphism, if $H≤G$ with $\ker(\phi)⊆H$, then $∀g∈G,∀h∈H,ghg^{-1}∈H$.

Published on 28 Jul 2020 - 23:02

score 290 · Answer 14 · 2016-07-10 08:01:12

290

Views

Homomorphism between a group of exponent $m$ and $\mathbb{Z}/m\mathbb{Z}$

Published on 10 Jul 2016 - 8:01

score 347 · Answer 15 · 2016-07-19 12:32:57

347

Views

To show that the endomorphism ring of any locally cyclic group is commutative

Published on 19 Jul 2016 - 12:32

List Question

(When) is this homomorphism an isomorphism?

A doubt about Proposition $27$ in textbook Algebra by Saunders MacLane and Garrett Birkhoff

Any morphism $\phi:G \rightarrow A$ to an abelian group $A$ factors uniquely through the projection $G \rightarrow G /[G,G]$.

Prove that $\phi: G / F \rightarrow \operatorname{Sym}(X)$ is a monomorphism

Homomorphic Image of ideal in Lie algebras

A simple proof of Sylow theorem for abelian groups

Question about the definition of tensor product of homomorphisms

Let $\varphi: G\rightarrow G'$ be a homomorphism. Show that for each $a \in G$, $| \varphi (a) | \le | a |$.

Sgn is a homomorphism of $S_n$ onto $\mu_2(Q)$ - proof

Describing homomorphisms from $\Bbb Z_n$ to $D_m$.

Prove that $\Bbb Q$ is an injective object in $\Bbb Z\text{-mod}$ using the following definition.

Homomorphism from $\mathbb{Z}_{120}$ to $\mathbb{Z}_{167}$

For groups $G,\bar{G},H$; $H$ abelian; and $\phi:G\to\bar{G}$, a homomorphism, if $H≤G$ with $\ker(\phi)⊆H$, then $∀g∈G,∀h∈H,ghg^{-1}∈H$.

Homomorphism between a group of exponent $m$ and $\mathbb{Z}/m\mathbb{Z}$

To show that the endomorphism ring of any locally cyclic group is commutative

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