Question

How to find $\left|\operatorname{Aut}(\mathbb Z_2\times\mathbb Z_2)\right|$

score 257 · Answer 1 · 2015-04-20 12:08:47

257

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How to find $\left|\operatorname{Aut}(\mathbb Z_2\times\mathbb Z_2)\right|$

Published on 20 Apr 2015 - 12:08

score 241 · Answer 2 · 2015-04-20 13:51:52

241

Views

Homomorphisms preserve solubility of groups, and some others.

Published on 20 Apr 2015 - 13:51

score 129 · Answer 3 · 2015-04-22 16:58:51

Let $\varphi$ be a group homomorphism from $G$ to $H$. Let $\varphi(G)$ be its image and $K$ its kernel. Show that $K$ is a normal divisor of $G$.

score 502 · Answer 4 · 2026-03-30 10:13:26

502

Views

Wanted: Group homomorphism $\operatorname{Aut}(G) \to H$ whose kernel is the set of inner automorphisms

Published on 30 Mar 2026 - 10:13

score 15.1k · Answer 5 · 2015-04-26 02:00:30

15.1k

Views

What does it mean for something to hold "up to isomorphism"?

Published on 26 Apr 2015 - 2:00

score 67 · Answer 6 · 2015-04-27 07:14:40

67

Views

There exists a homomorphism $f : G \to H$ with $|G| = 20$ and $|im f | = 6$

Published on 27 Apr 2015 - 7:14

score 127 · Answer 7 · 2026-03-30 10:11:31

127

Views

Finding Homomorphisms From a Cyclic Group to an Automorphism Group.

Published on 30 Mar 2026 - 10:11

score 809 · Answer 8 · 2015-04-28 08:42:18

809

Views

Action of $G$ on the left cosets of $H$ giving a non-trivial homomorphism

Published on 28 Apr 2015 - 8:42

score 304 · Answer 9 · 2015-04-29 00:36:35

304

Views

Is there a homomorphism from the general linear group of order n to the real numbers?

Published on 29 Apr 2015 - 0:36

score 1.2k · Answer 10 · 2015-05-01 12:26:12

1.2k

Views

Prove that if G has a faithful complex irreducible representation

Published on 01 May 2015 - 12:26

score 114 · Answer 11 · 2015-05-02 13:02:50

114

Views

Find an example of a group morphism

Published on 02 May 2015 - 13:02

score 81 · Answer 12 · 2015-05-05 15:11:09

81

Views

If $H\unlhd SL(2,\mathbb{Z})$ and $[SL(2,\mathbb{Z}):H]<\infty$ s.t. $H=\ker(\rho)$, then why is $|\operatorname{Im}(\rho)|<\infty$?

Published on 05 May 2015 - 15:11

score 77 · Answer 13 · 2015-05-09 06:54:34

77

Views

Homomorphisms and Groups proof

Published on 09 May 2015 - 6:54

score 56 · Answer 14 · 2015-05-11 07:25:46

56

Views

Homomorphisms Groups Kernel

Published on 11 May 2015 - 7:25

score 575 · Answer 15 · 2015-05-11 12:33:57

575

Views

What automorphisms exist on the abelian group of positive rationals under multiplication?

Published on 11 May 2015 - 12:33

List Question

How to find $\left|\operatorname{Aut}(\mathbb Z_2\times\mathbb Z_2)\right|$

Homomorphisms preserve solubility of groups, and some others.

Let $\varphi$ be a group homomorphism from $G$ to $H$. Let $\varphi(G)$ be its image and $K$ its kernel. Show that $K$ is a normal divisor of $G$.

Wanted: Group homomorphism $\operatorname{Aut}(G) \to H$ whose kernel is the set of inner automorphisms

What does it mean for something to hold "up to isomorphism"?

There exists a homomorphism $f : G \to H$ with $|G| = 20$ and $|im f | = 6$

Finding Homomorphisms From a Cyclic Group to an Automorphism Group.

Action of $G$ on the left cosets of $H$ giving a non-trivial homomorphism

Is there a homomorphism from the general linear group of order n to the real numbers?

Prove that if G has a faithful complex irreducible representation

Find an example of a group morphism

If $H\unlhd SL(2,\mathbb{Z})$ and $[SL(2,\mathbb{Z}):H]<\infty$ s.t. $H=\ker(\rho)$, then why is $|\operatorname{Im}(\rho)|<\infty$?

Homomorphisms and Groups proof

Homomorphisms Groups Kernel

What automorphisms exist on the abelian group of positive rationals under multiplication?

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