List questions from group-homomorphism

Published on 17 Apr 2017 - 1:07

68

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Show there is a group homomorphism

Published on 18 Apr 2017 - 5:32

1.1k

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Given $\phi:G\to G_1$ a homomorphism, prove $\ker(\phi)=G$

Published on 19 Apr 2017 - 19:43

331

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Show that If $\phi$ is a homomorphism, then $\phi(a^{-1}) = [\phi (a)]^{-1}$

Published on 20 Apr 2017 - 9:18

1.3k

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How to prove that the sum of matrices of two linear maps, $Mμ+Mv$, equals to the matrix of sum of two linear maps $M(μ+v)$？

Published on 22 Apr 2017 - 18:31

399

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Extending a map to a well defined homomorphism

Published on 27 Mar 2026 - 22:30

36

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Let $k: = \mathbb{Q} (ς)$ and $K: = k [\sqrt[3]{2}]$. Show that $K\cong k [X] / <X^3-2>$ and $K\otimes_k K\cong K\times K\times K$.

Published on 23 Apr 2017 - 22:49

114

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Homomorphism and group element orders

Published on 24 Apr 2017 - 14:47

288

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determine the elements in a kernel

Published on 25 Apr 2017 - 5:45

195

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Existence of isomorphisms between elliptic curves

Published on 27 Apr 2017 - 20:03

1.7k

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are all homomorphic groups of the same size isomorphic?

Published on 27 Apr 2017 - 20:33

102

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There exists a homomorphism $\sigma$ from $[a]$ to $[b]$ such that $\sigma(a)=b^k$

Published on 28 Apr 2017 - 11:39

518

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If a group homomorphism $f: \Bbb F \to\Bbb C^*$ has $f(ax)=f(bx)$ then $a=b$

Published on 29 Apr 2017 - 23:43

374

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defining group homomorphisms in terms of generators

Published on 01 May 2017 - 21:27

513

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isomorphic extension fields of the $p$-adic numbers

Published on 02 May 2017 - 14:57

List Question

Is there a way to symbolically denote a Homomorphism?

Show there is a group homomorphism

Given $\phi:G\to G_1$ a homomorphism, prove $\ker(\phi)=G$

Show that If $\phi$ is a homomorphism, then $\phi(a^{-1}) = [\phi (a)]^{-1}$

How to prove that the sum of matrices of two linear maps, $Mμ+Mv$, equals to the matrix of sum of two linear maps $M(μ+v)$？

Extending a map to a well defined homomorphism

Let $k: = \mathbb{Q} (ς)$ and $K: = k [\sqrt[3]{2}]$. Show that $K\cong k [X] / <X^3-2>$ and $K\otimes_k K\cong K\times K\times K$.

Homomorphism and group element orders

determine the elements in a kernel

Existence of isomorphisms between elliptic curves

are all homomorphic groups of the same size isomorphic?

There exists a homomorphism $\sigma$ from $[a]$ to $[b]$ such that $\sigma(a)=b^k$

If a group homomorphism $f: \Bbb F \to\Bbb C^*$ has $f(ax)=f(bx)$ then $a=b$

defining group homomorphisms in terms of generators

isomorphic extension fields of the $p$-adic numbers

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