Question

If $G$ is a group of order $p + 1$, then $p$ does not divide $|\text{Aut}(G)|$ ($p$ is prime and $p + 1$ isn't a prime power)

score 153 · Answer 1 · 2022-06-09 16:48:42

153

Views

If $G$ is a group of order $p + 1$, then $p$ does not divide $|\text{Aut}(G)|$ ($p$ is prime and $p + 1$ isn't a prime power)

Published on 09 Jun 2022 - 16:48

score 78 · Answer 2 · 2026-03-28 14:56:55

78

Views

Prove if $G$ is a finite nonabelian $p$-group, then $p^2\mid |{\rm Aut}(G)|$.

Published on 28 Mar 2026 - 14:56

score 40 · Answer 3 · 2022-06-12 17:53:06

40

Views

A field automorphism that is the identity outside a subfield

Published on 12 Jun 2022 - 17:53

score 95 · Answer 4 · 2022-06-16 17:55:29

95

Views

Let $p$ be the smallest prime divisor of $|G|$ and $N\unlhd G $ s.t. $|N|=p$. Find ${\rm Aut}(N)$.

Published on 16 Jun 2022 - 17:55

score 102 · Answer 5 · 2022-06-25 16:54:37

102

Views

Find the order of the following elements in ${\rm Inn}(S_5)$

Published on 25 Jun 2022 - 16:54

score 1k · Answer 6 · 2022-07-03 22:30:54

1k

Views

What is the automorphism group of a complete bipartite graph?

Published on 03 Jul 2022 - 22:30

score 260 · Answer 7 · 2022-07-16 16:12:30

260

Views

Is true any group is the automorphism group of itself?

Published on 16 Jul 2022 - 16:12

score 71 · Answer 8 · 2022-07-16 22:00:36

71

Views

About an automorphism of $\mathbb{Z}/4\mathbb{Z}$

Published on 16 Jul 2022 - 22:00

score 64 · Answer 9 · 2026-03-29 14:58:52

64

Views

About using conjugation in $S_4$ to help in finding the outer automorphisms of $D_4$

Published on 29 Mar 2026 - 14:58

score 203 · Answer 10 · 2022-07-20 12:19:54

203

Views

How many automorphisms does $C_{n}$ have?

Published on 20 Jul 2022 - 12:19

score 225 · Answer 11 · 2022-07-22 05:03:40

225

Views

Find pair of product of four groups that has the same order, but not isomorphic.

Published on 22 Jul 2022 - 5:03

score 120 · Answer 12 · 2026-03-25 23:35:40

120

Views

compute group automorphisms using magma

Published on 25 Mar 2026 - 23:35

score 83 · Answer 13 · 2026-03-25 23:35:45

83

Views

compute group automorphisms, part 2

Published on 25 Mar 2026 - 23:35

score 99 · Answer 14 · 2022-07-31 17:32:41

99

Views

Finding all group homomorphisms $\varphi:\mathbb{Z}/4\mathbb{Z} \to \text{Aut}(\mathbb{Z}/5\mathbb{Z})$

Published on 31 Jul 2022 - 17:32

score 73 · Answer 15 · 2026-03-28 05:22:05

73

Views

Transpose of automorphisms

Published on 28 Mar 2026 - 5:22

List Question

If $G$ is a group of order $p + 1$, then $p$ does not divide $|\text{Aut}(G)|$ ($p$ is prime and $p + 1$ isn't a prime power)

Prove if $G$ is a finite nonabelian $p$-group, then $p^2\mid |{\rm Aut}(G)|$.

A field automorphism that is the identity outside a subfield

Let $p$ be the smallest prime divisor of $|G|$ and $N\unlhd G $ s.t. $|N|=p$. Find ${\rm Aut}(N)$.

Find the order of the following elements in ${\rm Inn}(S_5)$

What is the automorphism group of a complete bipartite graph?

Is true any group is the automorphism group of itself?

About an automorphism of $\mathbb{Z}/4\mathbb{Z}$

About using conjugation in $S_4$ to help in finding the outer automorphisms of $D_4$

How many automorphisms does $C_{n}$ have?

Find pair of product of four groups that has the same order, but not isomorphic.

compute group automorphisms using magma

compute group automorphisms, part 2

Finding all group homomorphisms $\varphi:\mathbb{Z}/4\mathbb{Z} \to \text{Aut}(\mathbb{Z}/5\mathbb{Z})$

Transpose of automorphisms

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