Question

Minimal field extension of $\mathbb{Q}(\sqrt[6]{2})$ over $\mathbb{Q}$ and Galois group

score 421 · Answer 1 · 2026-03-28 15:20:09

421

Views

Minimal field extension of $\mathbb{Q}(\sqrt[6]{2})$ over $\mathbb{Q}$ and Galois group

Published on 28 Mar 2026 - 15:20

score 565 · Answer 2 · 2016-06-03 17:43:09

565

Views

Proving that if a finite group $G$ has a composition series of length 2, then any composition series has length 2

Published on 03 Jun 2016 - 17:43

score 129 · Answer 3 · 2016-06-04 05:38:09

129

Views

suppose that $H \leq G$ and $N \unlhd G$ and $(|H|,|G:N|) = 1$ then prove that $H \leq N$

Published on 04 Jun 2016 - 5:38

score 23 · Answer 4 · 2016-06-04 08:33:46

23

Views

Normal subgroup related

Published on 04 Jun 2016 - 8:33

score 857 · Answer 5 · 2016-06-04 09:35:15

857

Views

Normal subgroup of a finite group of order 21

Published on 04 Jun 2016 - 9:35

score 156 · Answer 6 · 2016-06-04 12:02:46

156

Views

Normalizer of some subgroup of a group is necessarily normal subgroup of the group.

Published on 04 Jun 2016 - 12:02

score 182 · Answer 7 · 2016-06-05 13:20:07

182

Views

$H\cap K$ is normal maximal subgroup of $H$.

Published on 05 Jun 2016 - 13:20

score 3.3k · Answer 8 · 2016-06-05 17:55:05

3.3k

Views

Let $G=\langle \mathbb{Z},+\rangle $ and $H=\{6n|n \in \mathbb{Z}\}$. Find all the distinct left and right cosets of $H$ in $G$.

Published on 05 Jun 2016 - 17:55

score 633 · Answer 9 · 2016-06-07 09:37:48

633

Views

We Quotient an algebraic structure to generate equivalence classes?

Published on 07 Jun 2016 - 9:37

score 463 · Answer 10 · 2026-04-01 17:28:50

463

Views

If $\phi: G \rightarrow H$ is a group homomorphism, $N \vartriangleleft G$, then $G/N \cong \phi(G)/\phi(N)$

Published on 01 Apr 2026 - 17:28

score 850 · Answer 11 · 2016-06-10 05:55:32

850

Views

Group of order $54$ has normal sugroup of order $27.$

Published on 10 Jun 2016 - 5:55

score 121 · Answer 12 · 2026-03-28 01:18:46

121

Views

Finding groups $H$ for which there exists surjective homomorphisms $f:D_4 \rightarrow H$?

Published on 28 Mar 2026 - 1:18

score 3.8k · Answer 13 · 2016-06-14 03:53:37

3.8k

Views

If a subgroup has smallest prime index, then it is normal

Published on 14 Jun 2016 - 3:53

score 780 · Answer 14 · 2016-06-16 08:18:57

780

Views

Index of intersection of two normal subgroups

Published on 16 Jun 2016 - 8:18

score 817 · Answer 15 · 2026-04-02 23:18:45

817

Views

A question on identifying normal subgroups of $S_4$

Published on 02 Apr 2026 - 23:18

List Question

Minimal field extension of $\mathbb{Q}(\sqrt[6]{2})$ over $\mathbb{Q}$ and Galois group

Proving that if a finite group $G$ has a composition series of length 2, then any composition series has length 2

suppose that $H \leq G$ and $N \unlhd G$ and $(|H|,|G:N|) = 1$ then prove that $H \leq N$

Normal subgroup related

Normal subgroup of a finite group of order 21

Normalizer of some subgroup of a group is necessarily normal subgroup of the group.

$H\cap K$ is normal maximal subgroup of $H$.

Let $G=\langle \mathbb{Z},+\rangle $ and $H=\{6n|n \in \mathbb{Z}\}$. Find all the distinct left and right cosets of $H$ in $G$.

We Quotient an algebraic structure to generate equivalence classes?

If $\phi: G \rightarrow H$ is a group homomorphism, $N \vartriangleleft G$, then $G/N \cong \phi(G)/\phi(N)$

Group of order $54$ has normal sugroup of order $27.$

Finding groups $H$ for which there exists surjective homomorphisms $f:D_4 \rightarrow H$?

If a subgroup has smallest prime index, then it is normal

Index of intersection of two normal subgroups

A question on identifying normal subgroups of $S_4$

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