Question

Given that $G/H=\{xH:x \in G\}$ is group under operation $(xH)(yH)=(xyH)$ . Then $H$ is normal subgroup of $G$

score 638 · Answer 1 · 2026-03-25 14:35:54

638

Views

Given that $G/H=\{xH:x \in G\}$ is group under operation $(xH)(yH)=(xyH)$ . Then $H$ is normal subgroup of $G$

Published on 25 Mar 2026 - 14:35

score 64 · Answer 2 · 2026-03-25 03:00:31

64

Views

Onto Algebra homomorphism between group rings.

Published on 25 Mar 2026 - 3:00

score 268 · Answer 3 · 2026-03-26 13:00:48

268

Views

What is the number of squares in $S_n$?

Published on 26 Mar 2026 - 13:00

score 51 · Answer 4 · 2026-03-27 09:37:41

51

Views

Prove that two groups act in the same way

Published on 27 Mar 2026 - 9:37

score 252 · Answer 5 · 2026-03-25 04:43:36

252

Views

Prove $H$ is a proper normal subgroup of $G$ if $H$ is generated by $\{[x,y] \mid x,y \in G\} \cup \{x^p \mid x \in G\}$.

Published on 25 Mar 2026 - 4:43

score 611 · Answer 6 · 2026-03-25 20:36:37

611

Views

Show that a group of order 66 has a normal subgroup of order 33.

Published on 25 Mar 2026 - 20:36

score 427 · Answer 7 · 2026-03-25 11:04:50

427

Views

Finding the number of subgroups of $\mathbb{Z}_{p^3} \oplus \mathbb{Z}_{p^2} $.

Published on 25 Mar 2026 - 11:04

score 150 · Answer 8 · 2026-03-25 06:03:51

150

Views

Presentation of $A_5 \times \Bbb Z_2$.

Published on 25 Mar 2026 - 6:03

score 2.2k · Answer 9 · 2026-03-26 10:59:58

2.2k

Views

What is the relationship between the orbit-stabilizer theorem and Lagrange's theorem?

Published on 26 Mar 2026 - 10:59

score 77 · Answer 10 · 2026-03-25 22:26:57

77

Views

What is the sufficient and necessary conditions that $-1 \in G$, where $G$ is a multiplicative group of a ring.

Published on 25 Mar 2026 - 22:26

score 1.8k · Answer 11 · 2026-03-27 09:37:39

1.8k

Views

Regarding $|\textrm{G}| = 65$ $\Rightarrow$ $\textrm{G}$ is cyclic.

Published on 27 Mar 2026 - 9:37

score 106 · Answer 12 · 2018-12-31 14:05:20

106

Views

Let $G=G_1\times G_2$, prove $G'=G_1'\times G_2'$

Published on 31 Dec 2018 - 14:05

score 212 · Answer 13 · 2018-12-31 18:42:56

212

Views

Lagrange's Theorem: Injectivity.

Published on 31 Dec 2018 - 18:42

score 197 · Answer 14 · 2026-03-25 01:17:17

197

Views

No onto map between group algebras $FS_5$ onto $M_6(F)$.

Published on 25 Mar 2026 - 1:17

score 258 · Answer 15 · 2019-01-01 07:14:29

258

Views

Burnsides Theorem Application - Necklace

Published on 01 Jan 2019 - 7:14

List Question

Given that $G/H=\{xH:x \in G\}$ is group under operation $(xH)(yH)=(xyH)$ . Then $H$ is normal subgroup of $G$

Onto Algebra homomorphism between group rings.

What is the number of squares in $S_n$?

Prove that two groups act in the same way

Prove $H$ is a proper normal subgroup of $G$ if $H$ is generated by $\{[x,y] \mid x,y \in G\} \cup \{x^p \mid x \in G\}$.

Show that a group of order 66 has a normal subgroup of order 33.

Finding the number of subgroups of $\mathbb{Z}_{p^3} \oplus \mathbb{Z}_{p^2} $.

Presentation of $A_5 \times \Bbb Z_2$.

What is the relationship between the orbit-stabilizer theorem and Lagrange's theorem?

What is the sufficient and necessary conditions that $-1 \in G$, where $G$ is a multiplicative group of a ring.

Regarding $|\textrm{G}| = 65$ $\Rightarrow$ $\textrm{G}$ is cyclic.

Let $G=G_1\times G_2$, prove $G'=G_1'\times G_2'$

Lagrange's Theorem: Injectivity.

No onto map between group algebras $FS_5$ onto $M_6(F)$.

Burnsides Theorem Application - Necklace

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