Question

Show that if $\frac {k!} {2} \lt n,$ then $G$ has a non-trivial proper normal subgroup.

score 69 · Answer 1 · 2020-09-14 16:23:44

69

Views

Show that if $\frac {k!} {2} \lt n,$ then $G$ has a non-trivial proper normal subgroup.

Published on 14 Sep 2020 - 16:23

score 51 · Answer 2 · 2020-09-15 15:25:58

51

Views

Let $\phi : A \rightarrow A/B$ be a homomorphism of groups, is $B \subset \ker$ $\phi $?

Published on 15 Sep 2020 - 15:25

score 1.2k · Answer 3 · 2020-09-16 03:40:40

1.2k

Views

How do you prove two groups are isomorphic?

Published on 16 Sep 2020 - 3:40

score 115 · Answer 4 · 2020-09-16 12:28:06

115

Views

Prove/disprove: $p>3$ prime. There doesn't exist any $H\lhd S_p$, $|H|=p$, such that $S_p/H\cong S_{p-1}$.

Published on 16 Sep 2020 - 12:28

score 1.2k · Answer 5 · 2020-09-16 16:22:28

1.2k

Views

Clarification of relation between $SL(2,\mathbb{R})$ and $Sp(2,\mathbb{R})$

Published on 16 Sep 2020 - 16:22

score 104 · Answer 6 · 2026-03-25 17:42:01

104

Views

How to prove that there is not a monomorphism from Klein 4-group to $Z_6$(or a epimorphism from $Z_6$ to $V_4$)?

Published on 25 Mar 2026 - 17:42

score 136 · Answer 7 · 2026-03-28 01:13:28

136

Views

Prove that $\mathbb{Z} / \mathrm{Ker}$ $f$ is isomorphic to $\mathrm{f}(\mathbb{Z} )$

Published on 28 Mar 2026 - 1:13

score 662 · Answer 8 · 2020-09-17 17:36:38

662

Views

Is ${G}/\ker(\phi)$ uniquely isomorphic to $\phi(G)$?

Published on 17 Sep 2020 - 17:36

score 100 · Answer 9 · 2026-03-27 19:31:04

100

Views

proving group is infinite

Published on 27 Mar 2026 - 19:31

score 104 · Answer 10 · 2020-09-19 02:39:59

104

Views

Homomorphism $\mathbb{Z} \to \mathbb{Z}/3\mathbb{Z}$

Published on 19 Sep 2020 - 2:39

score 155 · Answer 11 · 2020-09-20 19:24:47

155

Views

Prove that a map is one-to-one if $G$ is finite group and $H$ and $K$ are its subgroups

Published on 20 Sep 2020 - 19:24

score 831 · Answer 12 · 2020-09-22 12:21:01

831

Views

Set of Homomorphisms between two abelian groups is a group

Published on 22 Sep 2020 - 12:21

score 657 · Answer 13 · 2026-03-28 01:48:48

657

Views

Find the number of homomorphisms from $Z_m$ to $S_n$

Published on 28 Mar 2026 - 1:48

score 2k · Answer 14 · 2026-03-31 06:04:48

2k

Views

Inner automorphism group as the kernel of a homomorphism

Published on 31 Mar 2026 - 6:04

score 58 · Answer 15 · 2020-09-24 18:26:42

58

Views

What does a homomorphism have to do with the order of an element in a group?

Published on 24 Sep 2020 - 18:26

List Question

Show that if $\frac {k!} {2} \lt n,$ then $G$ has a non-trivial proper normal subgroup.

Let $\phi : A \rightarrow A/B$ be a homomorphism of groups, is $B \subset \ker$ $\phi $?

How do you prove two groups are isomorphic?

Prove/disprove: $p>3$ prime. There doesn't exist any $H\lhd S_p$, $|H|=p$, such that $S_p/H\cong S_{p-1}$.

Clarification of relation between $SL(2,\mathbb{R})$ and $Sp(2,\mathbb{R})$

How to prove that there is not a monomorphism from Klein 4-group to $Z_6$(or a epimorphism from $Z_6$ to $V_4$)?

Prove that $\mathbb{Z} / \mathrm{Ker}$ $f$ is isomorphic to $\mathrm{f}(\mathbb{Z} )$

Is ${G}/\ker(\phi)$ uniquely isomorphic to $\phi(G)$?

proving group is infinite

Homomorphism $\mathbb{Z} \to \mathbb{Z}/3\mathbb{Z}$

Prove that a map is one-to-one if $G$ is finite group and $H$ and $K$ are its subgroups

Set of Homomorphisms between two abelian groups is a group

Find the number of homomorphisms from $Z_m$ to $S_n$

Inner automorphism group as the kernel of a homomorphism

What does a homomorphism have to do with the order of an element in a group?

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