Question

Show $(G\times H)/(K\times K') \cong G/K\times H/K'$ if $K\lhd G$ and $K'\lhd H$

score 76 · Answer 1 · 2026-03-28 03:03:04

Show $(G\times H)/(K\times K') \cong G/K\times H/K'$ if $K\lhd G$ and $K'\lhd H$

Published on 28 Mar 2026 - 3:03

score 95 · Answer 2 · 2020-10-19 03:49:08

Let $h :\Bbb Z_{5}\rightarrow S_{z_{5}}$ be the left-regular representation of $\Bbb Z_5$? For each $n$ in $\Bbb Z_5$, compute $h(1)(n)$and $h(3)(n)$.

score 76 · Answer 3 · 2020-10-19 10:28:59

76

Views

$\left(H_{i}\right)_{i \in I}$ is a family of normal subgroups, Show $G$ is isomorphic to at least one subgroup of $\prod_{i \in I} G / H_{i}$

Published on 19 Oct 2020 - 10:28

score 207 · Answer 4 · 2020-10-20 03:44:38

207

Views

Is $S_3$ isomorphic to anything other than $D_3$?

Published on 20 Oct 2020 - 3:44

score 1.1k · Answer 5 · 2026-04-03 03:38:09

1.1k

Views

Is $G/H$ isomorphic to $G'$ if there exists an homomorphism between $G$ and $G'$ and $H$ being a normal subgroup?

Published on 03 Apr 2026 - 3:38

score 35 · Answer 6 · 2020-10-21 10:23:39

35

Views

A linear transformation on $\mathbb{R}^n$ is an isomorphism

Published on 21 Oct 2020 - 10:23

score 56 · Answer 7 · 2020-10-22 19:10:31

56

Views

G does not have to be isomorphic to direct product of trivially intersecting normal subgroups of G

Published on 22 Oct 2020 - 19:10

score 223 · Answer 8 · 2020-10-22 19:38:53

223

Views

How to prove a bijection is "well defined" and "surjective" properly? (with an example)

Published on 22 Oct 2020 - 19:38

score 121 · Answer 9 · 2026-04-05 13:48:22

121

Views

Describe all possible groups of order 102, up to isomorphism. Without using semidirect product.

Published on 05 Apr 2026 - 13:48

score 110 · Answer 10 · 2026-03-31 08:12:04

110

Views

Does the cyclic group $C_n$ have the fewest automorphisms among groups of order $n$?

Published on 31 Mar 2026 - 8:12

score 587 · Answer 11 · 2026-03-28 16:57:57

587

Views

Show that the subgroup of $S_4=\langle (12),(13)(24)\rangle$ is isomorphic to dihedral group of order $8$

Published on 28 Mar 2026 - 16:57

score 97 · Answer 12 · 2020-10-25 12:43:01

97

Views

Show that the only subgroup of $G$ that contains all the elements of maximal order is $G$ itself.

Published on 25 Oct 2020 - 12:43

score 98 · Answer 13 · 2026-03-28 03:27:47

98

Views

Let $K\unlhd G$. Show $Z(G)K/K\le Z(G/K)$. (The Second Isomorphism Theorem, perhaps?)

Published on 28 Mar 2026 - 3:27

score 129 · Answer 14 · 2026-03-28 04:42:46

129

Views

Why is $\operatorname{Hom}\left(\bigoplus_{\mathbb{N}} \mathbb{Z}, \mathbb{Z} \right) \simeq \prod_{\mathbb{Z}} \mathbb{Z}$?

Published on 28 Mar 2026 - 4:42

score 149 · Answer 15 · 2026-03-31 10:37:57

149

Views

Defining an automorphism of $G/N$ using the automorphism defined on $G$.

Published on 31 Mar 2026 - 10:37

List Question

Show $(G\times H)/(K\times K') \cong G/K\times H/K'$ if $K\lhd G$ and $K'\lhd H$

Let $h :\Bbb Z_{5}\rightarrow S_{z_{5}}$ be the left-regular representation of $\Bbb Z_5$? For each $n$ in $\Bbb Z_5$, compute $h(1)(n)$and $h(3)(n)$.

$\left(H_{i}\right)_{i \in I}$ is a family of normal subgroups, Show $G$ is isomorphic to at least one subgroup of $\prod_{i \in I} G / H_{i}$

Is $S_3$ isomorphic to anything other than $D_3$?

Is $G/H$ isomorphic to $G'$ if there exists an homomorphism between $G$ and $G'$ and $H$ being a normal subgroup?

A linear transformation on $\mathbb{R}^n$ is an isomorphism

G does not have to be isomorphic to direct product of trivially intersecting normal subgroups of G

How to prove a bijection is "well defined" and "surjective" properly? (with an example)

Describe all possible groups of order 102, up to isomorphism. Without using semidirect product.

Does the cyclic group $C_n$ have the fewest automorphisms among groups of order $n$?

Show that the subgroup of $S_4=\langle (12),(13)(24)\rangle$ is isomorphic to dihedral group of order $8$

Show that the only subgroup of $G$ that contains all the elements of maximal order is $G$ itself.

Let $K\unlhd G$. Show $Z(G)K/K\le Z(G/K)$. (The Second Isomorphism Theorem, perhaps?)

Why is $\operatorname{Hom}\left(\bigoplus_{\mathbb{N}} \mathbb{Z}, \mathbb{Z} \right) \simeq \prod_{\mathbb{Z}} \mathbb{Z}$?

Defining an automorphism of $G/N$ using the automorphism defined on $G$.

Trending Questions

Popular # Hahtags

Popular Questions