Question

Why is no isomorphism possible from $(\Bbb Q^,\cdot)$ to $(\Bbb R^,\cdot)?$

score 55 · Answer 1 · 2016-06-26 15:04:44

55

Views

Why is no isomorphism possible from $(\Bbb Q^,\cdot)$ to $(\Bbb R^,\cdot)?$

Published on 26 Jun 2016 - 15:04

score 97 · Answer 2 · 2026-03-28 03:01:02

97

Views

Showing that $\phi$ is a homomorphism

Published on 28 Mar 2026 - 3:01

score 213 · Answer 3 · 2016-06-28 22:44:20

213

Views

Extension of mapping of subset to homomorphism

Published on 28 Jun 2016 - 22:44

score 82 · Answer 4 · 2016-07-05 06:24:08

82

Views

Problem in solving a question related to group homomorphism.

Published on 05 Jul 2016 - 6:24

score 298 · Answer 5 · 2016-07-05 09:08:30

298

Views

Existence of surjective map / homomorphism from an infinite group onto its symmetric group

Published on 05 Jul 2016 - 9:08

score 204 · Answer 6 · 2013-06-24 06:44:37

204

Views

Finite groups $G$ with epimomorphisms $\phi_1,\phi_2 : F_2 \rightarrow G$ s.t. $|\phi_1(x^{-1}y^{-1}xy)|\neq|\phi_2(x^{-1}y^{-1}xy)|$.

Published on 24 Jun 2013 - 6:44

score 98 · Answer 7 · 2013-06-26 21:29:14

98

Views

Homomorphism $f:S_{2009} \rightarrow S_{2009}$

Published on 26 Jun 2013 - 21:29

score 3.7k · Answer 8 · 2013-09-16 02:41:14

3.7k

Views

Let $\phi:G_1\to G_2$ be a group homomorphism. Show $\phi(g^{-1})=(\phi(g))^{-1}$.

Published on 16 Sep 2013 - 2:41

score 1.9k · Answer 9 · 2013-09-25 01:18:03

1.9k

Views

Define the dual group $\hat G$ as the set of all homs. from $G$ to $\Bbb C^*$, with pointwise multiplication. Show $\hat G$ is an abelian group.

Published on 25 Sep 2013 - 1:18

score 2.7k · Answer 10 · 2013-10-28 01:25:38

2.7k

Views

Subgroups containing kernel of group morphism to an abelian group are normal.

Published on 28 Oct 2013 - 1:25

score 119 · Answer 11 · 2013-12-31 08:14:59

119

Views

Let $M:G\to H$ be a homomorphism and let $x$ be in $G$. Suppose that $x$ has order $k$. Show that if $M$ is injective, then $|M(x)|=|x|$

Published on 31 Dec 2013 - 8:14

score 827 · Answer 12 · 2014-02-13 05:27:21

827

Views

Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$

Published on 13 Feb 2014 - 5:27

score 698 · Answer 13 · 2014-03-05 16:32:31

698

Views

Proving $f(a) = a^{-1}$ is a homomorphism iff $G$ is commutative

Published on 05 Mar 2014 - 16:32

score 66 · Answer 14 · 2014-03-06 04:31:18

66

Views

Group Homomorphisms (some questions about what I can and can't do)

Published on 06 Mar 2014 - 4:31

score 176 · Answer 15 · 2017-04-12 00:22:46

176

Views

Counting the number of homomorphisms

Published on 12 Apr 2017 - 0:22

List Question

Why is no isomorphism possible from $(\Bbb Q^,\cdot)$ to $(\Bbb R^,\cdot)?$

Showing that $\phi$ is a homomorphism

Extension of mapping of subset to homomorphism

Problem in solving a question related to group homomorphism.

Existence of surjective map / homomorphism from an infinite group onto its symmetric group

Finite groups $G$ with epimomorphisms $\phi_1,\phi_2 : F_2 \rightarrow G$ s.t. $|\phi_1(x^{-1}y^{-1}xy)|\neq|\phi_2(x^{-1}y^{-1}xy)|$.

Homomorphism $f:S_{2009} \rightarrow S_{2009}$

Let $\phi:G_1\to G_2$ be a group homomorphism. Show $\phi(g^{-1})=(\phi(g))^{-1}$.

Define the dual group $\hat G$ as the set of all homs. from $G$ to $\Bbb C^*$, with pointwise multiplication. Show $\hat G$ is an abelian group.

Subgroups containing kernel of group morphism to an abelian group are normal.

Let $M:G\to H$ be a homomorphism and let $x$ be in $G$. Suppose that $x$ has order $k$. Show that if $M$ is injective, then $|M(x)|=|x|$

Characterize the groups $G$ for which the map $\iota: G \to G$, sending $x \mapsto x^{-1}$ for all $x \in G$, is an automorphism of $G$

Proving $f(a) = a^{-1}$ is a homomorphism iff $G$ is commutative

Group Homomorphisms (some questions about what I can and can't do)

Counting the number of homomorphisms

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