Question

Suppose $H, K\lhd G$. Show that there exists a 1-1 homomorphism $\phi:G/(H\cap K)\rightarrow G/H \times G/K.$

score 52 · Answer 1 · 2026-03-30 05:26:47

52

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Suppose $H, K\lhd G$. Show that there exists a 1-1 homomorphism $\phi:G/(H\cap K)\rightarrow G/H \times G/K.$

Published on 30 Mar 2026 - 5:26

score 140 · Answer 2 · 2023-06-05 06:44:01

140

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Theorem 6 Corollary 2, Section 1.5 of Hungerford’s Abstract Algebra

Published on 05 Jun 2023 - 6:44

score 117 · Answer 3 · 2023-06-05 14:01:04

117

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Let $K$ be a normal sugroup of $G$, and $H$ a subgroup of $G$. Show that $K\cap H$ is a normal subgroup of $H$.

Published on 05 Jun 2023 - 14:01

score 244 · Answer 4 · 2026-03-30 05:30:08

244

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Prove/disprove: Let $G$ a simple infinite group $\implies$ $G$ doesn't have a proper subgroup of finite index.

Published on 30 Mar 2026 - 5:30

score 89 · Answer 5 · 2023-06-06 11:09:05

89

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Theorem 6 Corollary 4, Section 1.5 of Hungerford’s Abstract Algebra

Published on 06 Jun 2023 - 11:09

score 128 · Answer 6 · 2023-06-07 15:47:19

128

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Let $n \in \mathbb {N}$ and $G$ a group of order $4n+2$. Prove $G$ isn't simple.

Published on 07 Jun 2023 - 15:47

score 168 · Answer 7 · 2026-03-25 12:26:06

168

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Exercise 3, Section 1.5 of Hungerford’s Abstract Algebra

Published on 25 Mar 2026 - 12:26

score 96 · Answer 8 · 2026-03-25 12:25:36

96

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Exercise 4, Section 1.5 of Hungerford’s Abstract Algebra

Published on 25 Mar 2026 - 12:25

score 59 · Answer 9 · 2023-06-13 17:48:41

59

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If $N_1,\dotsb,N_r\lhd G$, then $\langle N_1\cup \dotsb\cup N_r\rangle =N_1\dotsb N_r$.

Published on 13 Jun 2023 - 17:48

score 69 · Answer 10 · 2026-03-27 01:50:46

69

Views

If $H$ has a normal complement then it has the character restriction property

Published on 27 Mar 2026 - 1:50

score 376 · Answer 11 · 2023-06-20 11:37:52

376

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Prove that $a$ commutes with every element of the group $G$.

Published on 20 Jun 2023 - 11:37

score 45 · Answer 12 · 2026-03-26 19:01:55

45

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Corollary of the First Theorem of Hall for finite soluble groups

Published on 26 Mar 2026 - 19:01

score 36 · Answer 13 · 2026-03-30 07:07:36

36

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The cardinality assertion of the correspondence theorem

Published on 30 Mar 2026 - 7:07

score 98 · Answer 14 · 2023-07-03 10:52:03

98

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If $A$ is a normal subgroup of $G$, then $A ⊴ C(A)$ where $C(A)$ is the centralizer of $A$.

Published on 03 Jul 2023 - 10:52

score 126 · Answer 15 · 2026-03-30 07:11:44

126

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Find the number of homomorphisms from $S_7$ to $A_8$

Published on 30 Mar 2026 - 7:11

List Question

Suppose $H, K\lhd G$. Show that there exists a 1-1 homomorphism $\phi:G/(H\cap K)\rightarrow G/H \times G/K.$

Theorem 6 Corollary 2, Section 1.5 of Hungerford’s Abstract Algebra

Let $K$ be a normal sugroup of $G$, and $H$ a subgroup of $G$. Show that $K\cap H$ is a normal subgroup of $H$.

Prove/disprove: Let $G$ a simple infinite group $\implies$ $G$ doesn't have a proper subgroup of finite index.

Theorem 6 Corollary 4, Section 1.5 of Hungerford’s Abstract Algebra

Let $n \in \mathbb {N}$ and $G$ a group of order $4n+2$. Prove $G$ isn't simple.

Exercise 3, Section 1.5 of Hungerford’s Abstract Algebra

Exercise 4, Section 1.5 of Hungerford’s Abstract Algebra

If $N_1,\dotsb,N_r\lhd G$, then $\langle N_1\cup \dotsb\cup N_r\rangle =N_1\dotsb N_r$.

If $H$ has a normal complement then it has the character restriction property

Prove that $a$ commutes with every element of the group $G$.

Corollary of the First Theorem of Hall for finite soluble groups

The cardinality assertion of the correspondence theorem

If $A$ is a normal subgroup of $G$, then $A ⊴ C(A)$ where $C(A)$ is the centralizer of $A$.

Find the number of homomorphisms from $S_7$ to $A_8$

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