Question

Proof Verification $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R}, +)$.

score 721 · Answer 1 · 2026-04-13 16:51:51

721

Views

Proof Verification $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R}, +)$.

Published on 13 Apr 2026 - 16:51

score 954 · Answer 2 · 2026-04-14 14:48:02

954

Views

Classify all subgroups of $\Bbb Z.$ Show that all but one of these are isomorphic to $\Bbb Z$ itself.

Published on 14 Apr 2026 - 14:48

score 518 · Answer 3 · 2026-04-14 04:18:32

518

Views

How to show that a group $G$ is isomorphic to a subgroup of $GL_2(\mathbb{R})$

Published on 14 Apr 2026 - 4:18

score 170 · Answer 4 · 2026-04-15 08:47:06

170

Views

To Show that all ﬁbers of this map has exactly $|H \cap K|$ elements and $|HK| = \frac{|H|\times|K|}{|H\cap K|}$

Published on 15 Apr 2026 - 8:47

score 45 · Answer 5 · 2026-04-15 02:31:24

45

Views

Proof Verification, extend $\varphi(x^n)=\varphi(x)^n$ for all $n\in\mathbb{Z}^+$ to all integers

Published on 15 Apr 2026 - 2:31

score 132 · Answer 6 · 2026-04-15 20:38:33

132

Views

Given $G,H_1,H_2$ finite abelian groups and $G\times H_1 \cong G\times H_2$ then $H_1 \cong H_2$

Published on 15 Apr 2026 - 20:38

score 127 · Answer 7 · 2026-04-13 09:10:08

127

Views

Show that $\operatorname{Aff}(3)$ is isomorphic to $S_3$, the symmetric group of all permutations of 3 objects.

Published on 13 Apr 2026 - 9:10

score 298 · Answer 8 · 2026-04-15 03:26:45

298

Views

Isomorphism classes and isometries

Published on 15 Apr 2026 - 3:26

score 65 · Answer 9 · 2026-04-12 08:41:55

65

Views

Proving Isomorphism Linear SubSpaces

Published on 12 Apr 2026 - 8:41

score 114 · Answer 10 · 2026-04-13 17:16:47

114

Views

Inner product and isomorphism

Published on 13 Apr 2026 - 17:16

score 290 · Answer 11 · 2026-04-10 20:35:55

290

Views

Structure transport using a bijection

Published on 10 Apr 2026 - 20:35

score 958 · Answer 12 · 2026-04-10 01:51:47

958

Views

A step of proof of fundamental theorem of homomorphism of groups

Published on 10 Apr 2026 - 1:51

score 204 · Answer 13 · 2026-04-11 03:51:29

204

Views

If $H$ and $K$ are conjugate in $G$, are their normalizers equal, or just isomorphic?

Published on 11 Apr 2026 - 3:51

score 302 · Answer 14 · 2026-04-14 01:07:35

302

Views

How we can find the symmetric group with least $n$ whose subgroup of it is isomorphic to $G$?

Published on 14 Apr 2026 - 1:07

score 24 · Answer 15 · 2026-04-15 15:47:36

24

Views

If $S,T\subseteq R$ing are multiplicative & $\forall x\in S,y\in T,\exists n,x^n\in T,y^n\in S$ then $\exists$ isomorphism:$S^{-1}R\to T^{-1}R$

Published on 15 Apr 2026 - 15:47

List Question

Proof Verification $(\mathbb{Q},+)$ is not isomorphic to $(\mathbb{R}, +)$.

Classify all subgroups of $\Bbb Z.$ Show that all but one of these are isomorphic to $\Bbb Z$ itself.

How to show that a group $G$ is isomorphic to a subgroup of $GL_2(\mathbb{R})$

To Show that all ﬁbers of this map has exactly $|H \cap K|$ elements and $|HK| = \frac{|H|\times|K|}{|H\cap K|}$

Proof Verification, extend $\varphi(x^n)=\varphi(x)^n$ for all $n\in\mathbb{Z}^+$ to all integers

Given $G,H_1,H_2$ finite abelian groups and $G\times H_1 \cong G\times H_2$ then $H_1 \cong H_2$

Show that $\operatorname{Aff}(3)$ is isomorphic to $S_3$, the symmetric group of all permutations of 3 objects.

Isomorphism classes and isometries

Proving Isomorphism Linear SubSpaces

Inner product and isomorphism

Structure transport using a bijection

A step of proof of fundamental theorem of homomorphism of groups

If $H$ and $K$ are conjugate in $G$, are their normalizers equal, or just isomorphic?

How we can find the symmetric group with least $n$ whose subgroup of it is isomorphic to $G$?

If $S,T\subseteq R$ing are multiplicative & $\forall x\in S,y\in T,\exists n,x^n\in T,y^n\in S$ then $\exists$ isomorphism:$S^{-1}R\to T^{-1}R$

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