List questions from group-isomorphism

Published on 02 Apr 2015 - 0:20

49

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Ring Isomorphisms

Published on 02 Apr 2015 - 0:55

396

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Prove there does not exist any epimorphism of $(\mathbb{Q}, +)$ onto $(\mathbb{Z}, +)$.

Published on 31 Mar 2026 - 3:34

485

Views

Can the Quotient Group $HK/K$ be Confusing?

Published on 05 Apr 2015 - 23:28

1.5k

Views

Group of Dirichlet Characters Modulo $q$ is Isomorphic to $(\mathbb{Z} / q\mathbb{Z})^*$

Published on 10 Apr 2015 - 2:22

10.9k

Views

When is a group isomorphic to a proper subgroup of itself?

Published on 01 Apr 2026 - 17:42

1k

Views

Let G be a group. Use the FHT (Fundamental Homomorphism Theorem) to prove that the quotient group G/{e} is isomorphic to G.

Published on 31 Mar 2026 - 10:13

167

Views

If $G$ is a finite group such that the Klein four group is a quotient of $G$ , then can we write $G$ as a union of three proper subgroups ?

Published on 01 Apr 2026 - 17:38

685

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Is $A_4$ isomorphic to $D_3\times \mathbb Z_2$?

Published on 01 Apr 2026 - 17:36

828

Views

Direct sum of Abelian groups and Isomorphism

Published on 21 Apr 2015 - 1:46

652

Views

Prove that $\Big|\frac{f(z)-f(w)}{f(z)-\overline{f(w)}}\Big|\le \Big|\frac{z-w}{z-\overline w}\Big|$

Published on 29 Mar 2026 - 11:08

38

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Universal property question

Published on 26 Mar 2026 - 17:42

15.1k

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

Published on 31 Mar 2026 - 10:07

431

Views

Proving that $D_{12}\cong S_3 \times C_2$

Published on 27 Apr 2015 - 11:57

333

Views

Finding a subgroup of an abelian group that is isomorphic to Z

Published on 29 Apr 2015 - 0:03

List Question

Show $\Bbb R$ and $\Bbb R[X]$ not isomorphic

Ring Isomorphisms

Prove there does not exist any epimorphism of $(\mathbb{Q}, +)$ onto $(\mathbb{Z}, +)$.

Can the Quotient Group $HK/K$ be Confusing?

Group of Dirichlet Characters Modulo $q$ is Isomorphic to $(\mathbb{Z} / q\mathbb{Z})^*$

When is a group isomorphic to a proper subgroup of itself?

Let G be a group. Use the FHT (Fundamental Homomorphism Theorem) to prove that the quotient group G/{e} is isomorphic to G.

If $G$ is a finite group such that the Klein four group is a quotient of $G$ , then can we write $G$ as a union of three proper subgroups ?

Is $A_4$ isomorphic to $D_3\times \mathbb Z_2$?

Direct sum of Abelian groups and Isomorphism

Prove that $\Big|\frac{f(z)-f(w)}{f(z)-\overline{f(w)}}\Big|\le \Big|\frac{z-w}{z-\overline w}\Big|$

Universal property question

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

Proving that $D_{12}\cong S_3 \times C_2$

Finding a subgroup of an abelian group that is isomorphic to Z

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