List questions from group-homomorphism

Published on 20 Jan 2020 - 23:47

483

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Cokernel within the Category of Groups

Published on 27 Mar 2026 - 17:15

159

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Number of homomorphisms $ \phi: _4 \to _4 $

Published on 26 Mar 2026 - 14:21

116

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Do $\epsilon,\hat\epsilon$ exist such that $\hat\epsilon\hat\theta=\theta\epsilon$?

Published on 23 Jan 2020 - 13:19

158

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Find the cardinality of the image of $\varphi.$

Published on 27 Jan 2020 - 7:51

562

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Let $\varphi:G\to H$ and $\psi:H\to K$ be homomorphisms. Show that $\ker(\varphi)\unlhd\ker(\psi\circ\varphi).$

Published on 27 Jan 2020 - 15:21

85

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An intuitive approach to a Lemma related to subgroups of quotient groups.

Published on 22 Mar 2026 - 4:26

71

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If $H$ is a group of order $6$ and $f:S_n\to H$ surjective homomorphism, then what is $n$?

Published on 02 Feb 2020 - 2:11

624

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All homomorphisms from $K_4$ to $S_3$

Published on 02 Feb 2020 - 17:26

161

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Determine non-trivial homomorhisms $\phi:\mathbb{Z}_{9}\to \mathbb{Z}_{12}$ and $\phi:\mathbb{Z}_{40}\to \mathbb{Z}_{28}$

Published on 05 Feb 2020 - 17:54

80

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Showing group action consists of homomorphisms

Published on 06 Feb 2020 - 21:34

533

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$f$ factors through $q$, where $q$ is the quotient map, and $f$ is a homomorphism.

Published on 26 Mar 2026 - 12:37

27

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Let $N\unlhd G$ with $[G:N]=3$. Find all non-trivial group homomorphisms $f:G\to\Bbb{Z}/n\Bbb{Z}$ for $n=2,3,...,10$ with $N\le\ker(f)$.

Published on 09 Feb 2020 - 17:01

409

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$S_7$ is isomorphic to subgroup of all those elements of of $S_8$ that sends $8$ to $8$

Published on 13 Feb 2020 - 13:23

275

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Proving that ${\rm Aut } G$ has an identity element

Published on 14 Feb 2020 - 8:00

List Question

Homomorphisms between matrix groups

Cokernel within the Category of Groups

Number of homomorphisms $ \phi: _4 \to _4 $

Do $\epsilon,\hat\epsilon$ exist such that $\hat\epsilon\hat\theta=\theta\epsilon$?

Find the cardinality of the image of $\varphi.$

Let $\varphi:G\to H$ and $\psi:H\to K$ be homomorphisms. Show that $\ker(\varphi)\unlhd\ker(\psi\circ\varphi).$

An intuitive approach to a Lemma related to subgroups of quotient groups.

If $H$ is a group of order $6$ and $f:S_n\to H$ surjective homomorphism, then what is $n$?

All homomorphisms from $K_4$ to $S_3$

Determine non-trivial homomorhisms $\phi:\mathbb{Z}_{9}\to \mathbb{Z}_{12}$ and $\phi:\mathbb{Z}_{40}\to \mathbb{Z}_{28}$

Showing group action consists of homomorphisms

$f$ factors through $q$, where $q$ is the quotient map, and $f$ is a homomorphism.

Let $N\unlhd G$ with $[G:N]=3$. Find all non-trivial group homomorphisms $f:G\to\Bbb{Z}/n\Bbb{Z}$ for $n=2,3,...,10$ with $N\le\ker(f)$.

$S_7$ is isomorphic to subgroup of all those elements of of $S_8$ that sends $8$ to $8$

Proving that ${\rm Aut } G$ has an identity element

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