Question

Find the quotient group $G/H$ of group $G = 15\mathbb{Z}_{18}$ by $H = 8\mathbb{Z}_{18}$

score 48 · Answer 1 · 2026-03-26 22:55:43

48

Views

Find the quotient group $G/H$ of group $G = 15\mathbb{Z}_{18}$ by $H = 8\mathbb{Z}_{18}$

Published on 26 Mar 2026 - 22:55

score 63 · Answer 2 · 2023-04-13 19:00:26

63

Views

Group isomorphism applied to sum of characters

Published on 13 Apr 2023 - 19:00

score 49 · Answer 3 · 2026-03-30 05:26:31

49

Views

Notation $NM/M$ in the second isomorphism theorem

Published on 30 Mar 2026 - 5:26

score 62 · Answer 4 · 2026-03-26 22:57:56

62

Views

Whether two groups in the form of infinite product are isomorphic

Published on 26 Mar 2026 - 22:57

score 102 · Answer 5 · 2026-03-26 19:02:47

102

Views

Prove that the image of an element $g \in G$ of order $k$ is a product of $n/k$ disjoint $k$-cycles in $S(G)$.

Published on 26 Mar 2026 - 19:02

score 119 · Answer 6 · 2026-04-01 00:09:42

119

Views

Prove that if $k\mid n$ that there exist subgroup $H\le D_n$ such that $H \cong D_k$.

Published on 01 Apr 2026 - 0:09

score 102 · Answer 7 · 2023-05-05 16:42:49

102

Views

Classification of finite groups such that every subgroup is a quotient group of the group by one of its subgroup.

Published on 05 May 2023 - 16:42

score 60 · Answer 8 · 2026-03-30 05:30:16

60

Views

Prove that every group of order 6 is isomorphic to $C_6$ or $S_3$

Published on 30 Mar 2026 - 5:30

score 207 · Answer 9 · 2023-05-09 20:54:41

207

Views

Prove group and opposite group are isomorphic.

Published on 09 May 2023 - 20:54

score 178 · Answer 10 · 2026-03-26 22:53:18

178

Views

Confusion about the difference between HN/N and H/N in the second isomorphism theorem

Published on 26 Mar 2026 - 22:53

score 266 · Answer 11 · 2026-03-30 05:25:23

266

Views

Doubt in the proof of the First Group Isomorphism Theorem

Published on 30 Mar 2026 - 5:25

score 165 · Answer 12 · 2026-03-26 07:30:52

165

Views

Determining whether two groups are isomorphic based on Wirtinger presentation

Published on 26 Mar 2026 - 7:30

score 121 · Answer 13 · 2026-03-26 07:38:47

121

Views

Normal subgroup of fundamental group of Klein Bottle

Published on 26 Mar 2026 - 7:38

score 42 · Answer 14 · 2023-05-20 16:39:05

42

Views

Why isn't $\phi$ onto? $\phi:F \to F: \phi(f)(x) \mapsto x \cdot f(x)$ where $F$ is the set of $R \to R$ functions that have derivatives of all orders

Published on 20 May 2023 - 16:39

score 105 · Answer 15 · 2023-05-28 16:20:45

105

Views

Proving there is one group of order $3$, up to isomorphism

Published on 28 May 2023 - 16:20

List Question

Find the quotient group $G/H$ of group $G = 15\mathbb{Z}_{18}$ by $H = 8\mathbb{Z}_{18}$

Group isomorphism applied to sum of characters

Notation $NM/M$ in the second isomorphism theorem

Whether two groups in the form of infinite product are isomorphic

Prove that the image of an element $g \in G$ of order $k$ is a product of $n/k$ disjoint $k$-cycles in $S(G)$.

Prove that if $k\mid n$ that there exist subgroup $H\le D_n$ such that $H \cong D_k$.

Classification of finite groups such that every subgroup is a quotient group of the group by one of its subgroup.

Prove that every group of order 6 is isomorphic to $C_6$ or $S_3$

Prove group and opposite group are isomorphic.

Confusion about the difference between HN/N and H/N in the second isomorphism theorem

Doubt in the proof of the First Group Isomorphism Theorem

Determining whether two groups are isomorphic based on Wirtinger presentation

Normal subgroup of fundamental group of Klein Bottle

Why isn't $\phi$ onto? $\phi:F \to F: \phi(f)(x) \mapsto x \cdot f(x)$ where $F$ is the set of $R \to R$ functions that have derivatives of all orders

Proving there is one group of order $3$, up to isomorphism

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