Question

Internal Semidirect with Factors Isomorphic to "Outside" Groups

score 35 · Answer 1 · 2026-03-25 09:24:10

35

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Internal Semidirect with Factors Isomorphic to "Outside" Groups

Published on 25 Mar 2026 - 9:24

score 2k · Answer 2 · 2026-03-22 11:13:07

2k

Views

Isomorphism between $GL_2(\mathbb{F}_2)$ and $S_3$

Published on 22 Mar 2026 - 11:13

score 91 · Answer 3 · 2019-03-21 00:35:36

91

Views

Proof explanation of $P(p^e) \cong \mathbb{Z}/(p-1)\mathbb{Z} \times \mathbb{Z}/(p^{e-1})\mathbb{Z}$.

Published on 21 Mar 2019 - 0:35

score 234 · Answer 4 · 2026-03-25 21:49:54

234

Views

Prove if the the groups $A_4$ and $S_3 \times \Bbb Z_2$ are or not are isomorphic

Published on 25 Mar 2026 - 21:49

score 956 · Answer 5 · 2026-03-26 19:37:23

956

Views

Question about the proof of Second Isomorphism Theorem

Published on 26 Mar 2026 - 19:37

score 355 · Answer 6 · 2026-03-26 23:09:18

355

Views

Similarities between the idea of Group Homomorphisms and Linear Transformations

Published on 26 Mar 2026 - 23:09

score 77 · Answer 7 · 2019-03-24 20:41:32

77

Views

Is $\prod_{i=1}^\infty \Bbb Z\times(\mathbb{Z}\times\Bbb Z)\cong \prod_{i=1}^\infty\Bbb Z\times(\Bbb Z)$ ? Yes/no

Published on 24 Mar 2019 - 20:41

score 1k · Answer 8 · 2019-03-25 23:51:05

1k

Views

Proving that something is an isomorphism between group generators.

Published on 25 Mar 2019 - 23:51

score 52 · Answer 9 · 2026-03-26 23:10:44

52

Views

If $H$ is a subgroup of $G$ and $a \in G$. Show that $H$ and $a^{-1}Ha$ are isomorphic.

Published on 26 Mar 2026 - 23:10

score 1k · Answer 10 · 2026-03-25 22:30:03

1k

Views

Splitting field/subfield is isomorphic

Published on 25 Mar 2026 - 22:30

score 77 · Answer 11 · 2019-03-28 21:40:15

77

Views

Number theory in Cryptography: Can I say two following subgroups are isomorphic?

Published on 28 Mar 2019 - 21:40

score 29 · Answer 12 · 2019-04-01 13:39:47

29

Views

Relation between the order of the elements of 2 groups and isomorphism

Published on 01 Apr 2019 - 13:39

score 136 · Answer 13 · 2026-03-26 21:27:11

136

Views

Homomorphism $\phi: G \rightarrow H$, $\phi$ surjective, $\exists a \in H : |a| = 5$, show $\exists x \in G : |x| = 5$

Published on 26 Mar 2026 - 21:27

score 60 · Answer 14 · 2019-04-03 20:12:43

60

Views

Prove $(G \times \mathbb{Z}_2)/K \cong G$ for $K = \{(e, 0), (g, 1)\}$ and $o(g) = 2$ with $g \in Z(G)$.

Published on 03 Apr 2019 - 20:12

score 351 · Answer 15 · 2019-04-05 14:52:39

351

Views

Should the isomorphism theorems be seen as an "interface" between algebra and category theory?

Published on 05 Apr 2019 - 14:52

List Question

Internal Semidirect with Factors Isomorphic to "Outside" Groups

Isomorphism between $GL_2(\mathbb{F}_2)$ and $S_3$

Proof explanation of $P(p^e) \cong \mathbb{Z}/(p-1)\mathbb{Z} \times \mathbb{Z}/(p^{e-1})\mathbb{Z}$.

Prove if the the groups $A_4$ and $S_3 \times \Bbb Z_2$ are or not are isomorphic

Question about the proof of Second Isomorphism Theorem

Similarities between the idea of Group Homomorphisms and Linear Transformations

Is $\prod_{i=1}^\infty \Bbb Z\times(\mathbb{Z}\times\Bbb Z)\cong \prod_{i=1}^\infty\Bbb Z\times(\Bbb Z)$ ? Yes/no

Proving that something is an isomorphism between group generators.

If $H$ is a subgroup of $G$ and $a \in G$. Show that $H$ and $a^{-1}Ha$ are isomorphic.

Splitting field/subfield is isomorphic

Number theory in Cryptography: Can I say two following subgroups are isomorphic?

Relation between the order of the elements of 2 groups and isomorphism

Homomorphism $\phi: G \rightarrow H$, $\phi$ surjective, $\exists a \in H : |a| = 5$, show $\exists x \in G : |x| = 5$

Prove $(G \times \mathbb{Z}_2)/K \cong G$ for $K = \{(e, 0), (g, 1)\}$ and $o(g) = 2$ with $g \in Z(G)$.

Should the isomorphism theorems be seen as an "interface" between algebra and category theory?

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