Question

Internal Semidirect with Factors Isomorphic to "Outside" Groups

score 38 · Answer 1 · 2026-05-10 21:52:14

38

Views

Internal Semidirect with Factors Isomorphic to "Outside" Groups

Published on 10 May 2026 - 21:52

score 2k · Answer 2 · 2026-05-01 21:59:08

2k

Views

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

Published on 01 May 2026 - 21:59

score 94 · Answer 3 · 2026-04-09 11:16:07

94

Views

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

Published on 09 Apr 2026 - 11:16

score 236 · Answer 4 · 2026-04-13 19:08:23

236

Views

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

Published on 13 Apr 2026 - 19:08

score 958 · Answer 5 · 2026-04-11 00:03:23

958

Views

Question about the proof of Second Isomorphism Theorem

Published on 11 Apr 2026 - 0:03

score 357 · Answer 6 · 2026-04-12 23:01:08

357

Views

Similarities between the idea of Group Homomorphisms and Linear Transformations

Published on 12 Apr 2026 - 23:01

score 80 · Answer 7 · 2026-04-13 23:21:14

80

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 13 Apr 2026 - 23:21

score 1k · Answer 8 · 2026-05-14 21:29:53

1k

Views

Proving that something is an isomorphism between group generators.

Published on 14 May 2026 - 21:29

score 54 · Answer 9 · 2026-04-12 14:11:04

54

Views

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

Published on 12 Apr 2026 - 14:11

score 1k · Answer 10 · 2026-04-09 19:48:18

1k

Views

Splitting field/subfield is isomorphic

Published on 09 Apr 2026 - 19:48

score 80 · Answer 11 · 2026-04-14 07:30:03

80

Views

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

Published on 14 Apr 2026 - 7:30

score 32 · Answer 12 · 2026-04-14 23:52:56

32

Views

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

Published on 14 Apr 2026 - 23:52

score 138 · Answer 13 · 2026-04-16 08:05:16

138

Views

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

Published on 16 Apr 2026 - 8:05

score 63 · Answer 14 · 2026-04-16 14:25:18

63

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 16 Apr 2026 - 14:25

score 354 · Answer 15 · 2026-04-13 08:36:06

354

Views

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

Published on 13 Apr 2026 - 8:36

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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