Question

Prove that $|\operatorname{Gal}(F(\lambda)/F)|=\left|\frac{\langle a \rangle}{\langle a \rangle \cap H}\right|.$

score 59 · Answer 1 · 2026-03-31 10:39:06

59

Views

Prove that $|\operatorname{Gal}(F(\lambda)/F)|=\left|\frac{\langle a \rangle}{\langle a \rangle \cap H}\right|.$

Published on 31 Mar 2026 - 10:39

score 129 · Answer 2 · 2026-03-28 04:42:46

129

Views

Why is $\operatorname{Hom}\left(\bigoplus_{\mathbb{N}} \mathbb{Z}, \mathbb{Z} \right) \simeq \prod_{\mathbb{Z}} \mathbb{Z}$?

Published on 28 Mar 2026 - 4:42

score 140 · Answer 3 · 2026-03-26 07:33:48

140

Views

Homomorphisms of a Semidirect Product

Published on 26 Mar 2026 - 7:33

score 164 · Answer 4 · 2026-03-28 20:57:20

164

Views

Abstract characterization of dihedral group

Published on 28 Mar 2026 - 20:57

score 78 · Answer 5 · 2020-10-29 17:18:57

78

Views

Bijection from $\mathrm{Hom}(\mathbb{Z}_2,G)$ to $H:=\{g\in G:g^2=e\}$

Published on 29 Oct 2020 - 17:18

score 112 · Answer 6 · 2020-11-01 20:07:32

112

Views

Let $f: (\mathbb{Z}_{24}, +) \rightarrow (\mathbb{Z}_{36}, +)$ be a group homomorphism. How many elements are there in the kernel of $f$?

Published on 01 Nov 2020 - 20:07

score 896 · Answer 7 · 2020-11-02 02:26:45

896

Views

If an homomorphism maps elements of the same orders to each other, is then an isomorphism?

Published on 02 Nov 2020 - 2:26

score 626 · Answer 8 · 2020-11-02 17:44:07

626

Views

Inverse of Homomorphism

Published on 02 Nov 2020 - 17:44

score 113 · Answer 9 · 2020-11-03 07:15:50

113

Views

Doubt in proving homomorphism from $S_n$

Published on 03 Nov 2020 - 7:15

score 163 · Answer 10 · 2020-11-03 15:45:18

163

Views

Does $[G,G] \trianglelefteq \text{ker}(\Psi)$ hold?

Published on 03 Nov 2020 - 15:45

score 61 · Answer 11 · 2026-03-27 04:00:04

61

Views

Proving that $G$-action on $R/I$ defined by ${}^g \pi(r) = \pi({}^gr)$ is a homomorphism.

Published on 27 Mar 2026 - 4:00

score 353 · Answer 12 · 2020-11-04 16:03:16

353

Views

Modulo Ring Homomorphisms

Published on 04 Nov 2020 - 16:03

score 125 · Answer 13 · 2020-11-04 16:25:27

125

Views

$|\phi^{-1}(\phi(H))| = |\ker \phi||\phi(H)|$ ? where $H \leq G$

Published on 04 Nov 2020 - 16:25

score 74 · Answer 14 · 2026-03-27 21:20:34

74

Views

Show that $G$ has finite index subgroup isomorphic to $\Bbb{Z}$ if there exists homomorphism $\Phi:G \rightarrow \Bbb{Z}$ with $\ker(\Phi)$ finite

Published on 27 Mar 2026 - 21:20

score 62 · Answer 15 · 2026-03-31 13:02:07

62

Views

Does existence of homomorphism imply there is $\psi$ with $\psi(ab) = \psi(b) \circ \psi(a)$

Published on 31 Mar 2026 - 13:02

List Question

Prove that $|\operatorname{Gal}(F(\lambda)/F)|=\left|\frac{\langle a \rangle}{\langle a \rangle \cap H}\right|.$

Why is $\operatorname{Hom}\left(\bigoplus_{\mathbb{N}} \mathbb{Z}, \mathbb{Z} \right) \simeq \prod_{\mathbb{Z}} \mathbb{Z}$?

Homomorphisms of a Semidirect Product

Abstract characterization of dihedral group

Bijection from $\mathrm{Hom}(\mathbb{Z}_2,G)$ to $H:=\{g\in G:g^2=e\}$

Let $f: (\mathbb{Z}_{24}, +) \rightarrow (\mathbb{Z}_{36}, +)$ be a group homomorphism. How many elements are there in the kernel of $f$?

If an homomorphism maps elements of the same orders to each other, is then an isomorphism?

Inverse of Homomorphism

Doubt in proving homomorphism from $S_n$

Does $[G,G] \trianglelefteq \text{ker}(\Psi)$ hold?

Proving that $G$-action on $R/I$ defined by ${}^g \pi(r) = \pi({}^gr)$ is a homomorphism.

Modulo Ring Homomorphisms

$|\phi^{-1}(\phi(H))| = |\ker \phi||\phi(H)|$ ? where $H \leq G$

Show that $G$ has finite index subgroup isomorphic to $\Bbb{Z}$ if there exists homomorphism $\Phi:G \rightarrow \Bbb{Z}$ with $\ker(\Phi)$ finite

Does existence of homomorphism imply there is $\psi$ with $\psi(ab) = \psi(b) \circ \psi(a)$

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