Question

Classify all groups of order 75

score 6k · Answer 1 · 2026-04-29 12:47:55

6k

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Classify all groups of order 75

Published on 29 Apr 2026 - 12:47

score 230 · Answer 2 · 2026-05-07 20:03:09

230

Views

Proof check, existence of free product

Published on 07 May 2026 - 20:03

score 1k · Answer 3 · 2026-05-10 13:26:30

1k

Views

Proof verification: Prove whether or not every proper subgroup of a nonabelian group is nonabelian.

Published on 10 May 2026 - 13:26

score 151 · Answer 4 · 2026-05-10 13:28:08

151

Views

Let $H\leq G$. If $g\in G$, show that $gHg^{-1}=\left \{ g^{-1}hg:h\in H,g\in G \right \}$ is a subgroup of $G$.

Published on 10 May 2026 - 13:28

score 1k · Answer 5 · 2026-04-14 12:54:01

1k

Views

Subgroups of General Linear Group

Published on 14 Apr 2026 - 12:54

score 1.4k · Answer 6 · 2026-05-10 13:27:18

1.4k

Views

Proof verification: If $xy=x^{-1}y^{-1}$ for all $x,y\in G$, then $G$ is abelian.

Published on 10 May 2026 - 13:27

score 259 · Answer 7 · 2026-05-07 10:09:20

259

Views

What is the identity element for the subgroup $H=\{a+b\sqrt{2}:a,b\in\mathbb{Q},\text{$a$ and $b$ are not both zero}\}$ of the group $\mathbb{R}^*$?

Published on 07 May 2026 - 10:09

score 2.7k · Answer 8 · 2026-05-10 13:51:01

2.7k

Views

True or False: Let $G, H$ be finite groups. Then any subgroup of $G × H$ is equal to $A × B$ for some subgroups $A<G$ and $B<H$.(TIFR GS2018)

Published on 10 May 2026 - 13:51

score 162 · Answer 9 · 2026-05-04 11:51:02

162

Views

Find the order of 5 in $\mathbb Z_{12}$

Published on 04 May 2026 - 11:51

score 1.6k · Answer 10 · 2026-04-17 13:52:17

1.6k

Views

Find a group G containing exactly 44 elements x s.t. x generates G

Published on 17 Apr 2026 - 13:52

score 330 · Answer 11 · 2026-04-14 16:29:52

330

Views

Third part of Sylow's theorem [from Herstein's book]

Published on 14 Apr 2026 - 16:29

score 322 · Answer 12 · 2026-04-29 12:42:46

322

Views

Cannot follow proof that refinement of solvable series is also solvable

Published on 29 Apr 2026 - 12:42

score 101 · Answer 13 · 2026-05-05 04:11:11

101

Views

Some conditions on a finite non-abelian $2$-group

Published on 05 May 2026 - 4:11

score 1.7k · Answer 14 · 2026-04-11 00:00:28

1.7k

Views

Importance of Normal subgroups

Published on 11 Apr 2026 - 0:00

score 46 · Answer 15 · 2026-05-10 15:51:34

46

Views

Why does $\mathbb{Z}/k\mathbb{Z}\cong\mathbb{Z}_{k}$ instead of homomorphism?

Published on 10 May 2026 - 15:51

List Question

Classify all groups of order 75

Proof check, existence of free product

Proof verification: Prove whether or not every proper subgroup of a nonabelian group is nonabelian.

Let $H\leq G$. If $g\in G$, show that $gHg^{-1}=\left \{ g^{-1}hg:h\in H,g\in G \right \}$ is a subgroup of $G$.

Subgroups of General Linear Group

Proof verification: If $xy=x^{-1}y^{-1}$ for all $x,y\in G$, then $G$ is abelian.

What is the identity element for the subgroup $H=\{a+b\sqrt{2}:a,b\in\mathbb{Q},\text{$a$ and $b$ are not both zero}\}$ of the group $\mathbb{R}^*$?

True or False: Let $G, H$ be finite groups. Then any subgroup of $G × H$ is equal to $A × B$ for some subgroups $A<G$ and $B<H$.(TIFR GS2018)

Find the order of 5 in $\mathbb Z_{12}$

Find a group G containing exactly 44 elements x s.t. x generates G

Third part of Sylow's theorem [from Herstein's book]

Cannot follow proof that refinement of solvable series is also solvable

Some conditions on a finite non-abelian $2$-group

Importance of Normal subgroups

Why does $\mathbb{Z}/k\mathbb{Z}\cong\mathbb{Z}_{k}$ instead of homomorphism?

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