Question

Automorphism group of cyclic group is isomorphic to $(\mathbb{Z}/n\mathbb{Z})^*$

score 1.1k · Answer 1 · 2026-04-01 12:15:16

1.1k

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Automorphism group of cyclic group is isomorphic to $(\mathbb{Z}/n\mathbb{Z})^*$

Published on 01 Apr 2026 - 12:15

score 84 · Answer 2 · 2021-10-19 21:00:49

84

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A composition law on $\mathbb{Z}/l\mathbb{Z}$

Published on 19 Oct 2021 - 21:00

score 210 · Answer 3 · 2021-10-21 12:47:43

210

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Find the number of generators for $(\mu_{25}, .)$

Published on 21 Oct 2021 - 12:47

score 347 · Answer 4 · 2026-03-29 10:08:51

347

Views

Show that dihedral group of twice odd order doesn't have a normal subgroup of order $2m$, where $m$ divides $n$.

Published on 29 Mar 2026 - 10:08

score 173 · Answer 5 · 2026-03-27 04:38:10

173

Views

The Sylow $2$-subgroups of $SL(2,q)$ are not cyclic for $q \equiv 3$ mod $4$?

Published on 27 Mar 2026 - 4:38

score 151 · Answer 6 · 2026-04-04 09:40:14

151

Views

How many homomorphisms are there from one group to another group?

Published on 04 Apr 2026 - 9:40

score 303 · Answer 7 · 2026-04-01 12:19:25

303

Views

Proof of $\operatorname{Aut}(C_p)\cong C_{p-1}$ by means of permutations?

Published on 01 Apr 2026 - 12:19

score 38 · Answer 8 · 2021-10-30 13:46:17

38

Views

How do I prove that the order of an element is p?

Published on 30 Oct 2021 - 13:46

score 156 · Answer 9 · 2026-03-28 00:28:53

156

Views

Given $A_8$, find a cyclic subgroup and a noncyclic subgroup, both with order 4.

Published on 28 Mar 2026 - 0:28

score 85 · Answer 10 · 2021-11-08 15:29:03

85

Views

Determine if the subgroup $\{(1),(15)(23),(12)(35),(13)(25)\}$ of $S_5$ is cyclic.

Published on 08 Nov 2021 - 15:29

score 54 · Answer 11 · 2021-11-09 17:56:32

54

Views

Let $G$ and $H$ be groups and $\varphi:G \to H$ a group isomorphism. Show that if $H$ is cyclic, then $G$ is cyclic also.

Published on 09 Nov 2021 - 17:56

score 1.6k · Answer 12 · 2021-11-11 23:19:58

1.6k

Views

If $H$ and $K$ are subgroups of prime order $p$, show that $H = K$ or $H \cap K = \{1\}$

Published on 11 Nov 2021 - 23:19

score 98 · Answer 13 · 2021-11-12 00:09:26

98

Views

An isomorphism between $U(13)$ and $\mathbb{Z}_3 \times \mathbb{Z}_4$

Published on 12 Nov 2021 - 0:09

score 248 · Answer 14 · 2021-11-12 19:29:44

248

Views

Are cyclic group generators guaranteed to keep generating all group elements, and why?

Published on 12 Nov 2021 - 19:29

score 51 · Answer 15 · 2026-02-26 21:50:46

51

Views

Problem on the cyclic group generated by $T(z)=e^{2i\pi\theta} z$ with $\theta$ irrational.

Published on 26 Feb 2026 - 21:50

List Question

Automorphism group of cyclic group is isomorphic to $(\mathbb{Z}/n\mathbb{Z})^*$

A composition law on $\mathbb{Z}/l\mathbb{Z}$

Find the number of generators for $(\mu_{25}, .)$

Show that dihedral group of twice odd order doesn't have a normal subgroup of order $2m$, where $m$ divides $n$.

The Sylow $2$-subgroups of $SL(2,q)$ are not cyclic for $q \equiv 3$ mod $4$?

How many homomorphisms are there from one group to another group?

Proof of $\operatorname{Aut}(C_p)\cong C_{p-1}$ by means of permutations?

How do I prove that the order of an element is p?

Given $A_8$, find a cyclic subgroup and a noncyclic subgroup, both with order 4.

Determine if the subgroup $\{(1),(15)(23),(12)(35),(13)(25)\}$ of $S_5$ is cyclic.

Let $G$ and $H$ be groups and $\varphi:G \to H$ a group isomorphism. Show that if $H$ is cyclic, then $G$ is cyclic also.

If $H$ and $K$ are subgroups of prime order $p$, show that $H = K$ or $H \cap K = \{1\}$

An isomorphism between $U(13)$ and $\mathbb{Z}_3 \times \mathbb{Z}_4$

Are cyclic group generators guaranteed to keep generating all group elements, and why?

Problem on the cyclic group generated by $T(z)=e^{2i\pi\theta} z$ with $\theta$ irrational.

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