Question

Confusing step in proof of property of cyclic group automorphisms

score 42 · Answer 1 · 2026-03-20 11:32:47

42

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Confusing step in proof of property of cyclic group automorphisms

Published on 20 Mar 2026 - 11:32

score 72 · Answer 2 · 2026-03-22 10:55:32

72

Views

If $G=\langle x\rangle$ is cyclic group and order of $G$ is $40$ then how many order of $x^3$

Published on 22 Mar 2026 - 10:55

score 58 · Answer 3 · 2026-03-19 18:17:56

58

Views

How to arrange $p-1$ non-zero elements into $A$ groups of $B$ where $p$ is a prime number

Published on 19 Mar 2026 - 18:17

score 52 · Answer 4 · 2026-03-22 09:33:10

52

Views

$e^{n/e}$ estimate of the maximum order of permutation group element: proof

Published on 22 Mar 2026 - 9:33

score 67 · Answer 5 · 2026-03-20 03:50:02

67

Views

Intuitive understanding of $g^iH=(gH)^i$ factor groups

Published on 20 Mar 2026 - 3:50

score 671 · Answer 6 · 2026-03-20 01:21:54

671

Views

Exams exercise involving the permutation group $S_5$

Published on 20 Mar 2026 - 1:21

score 154 · Answer 7 · 2026-03-20 18:45:50

154

Views

Find the order of 5 in $\mathbb Z_{12}$

Published on 20 Mar 2026 - 18:45

score 64 · Answer 8 · 2026-03-17 10:55:29

64

Views

The commutator of two subgroup in a finite group

Published on 17 Mar 2026 - 10:55

score 75 · Answer 9 · 2026-03-20 22:34:10

75

Views

Show that, for every $x\ \epsilon \ C_{m}$, we have that $ord(f(x))$ is a divisor of d.

Published on 20 Mar 2026 - 22:34

score 4.4k · Answer 10 · 2026-03-22 10:15:11

4.4k

Views

Why are $-1$ and $1$ generators for the Set of integers under addition?

Published on 22 Mar 2026 - 10:15

score 1.1k · Answer 11 · 2026-03-20 13:13:51

1.1k

Views

Proof verification: For all $g\in G$, with $G$ being a group, $|a|=|g^{-1}ag|$.

Published on 20 Mar 2026 - 13:13

score 489 · Answer 12 · 2026-03-25 06:02:09

489

Views

What is the difference between cyclic subgroup $\left \langle a\right \rangle$ and $\left \langle a^{k} \right \rangle$?

Published on 25 Mar 2026 - 6:02

score 143 · Answer 13 · 2026-03-25 02:05:16

143

Views

If $f:G→ℤ_{8}$ be a group epimorphism , then what can be said about $G$?

Published on 25 Mar 2026 - 2:05

score 160 · Answer 14 · 2026-03-25 06:05:36

160

Views

Proof verification: Show that the intersection of two generators is a subgroup of both individual generators.

Published on 25 Mar 2026 - 6:05

score 181 · Answer 15 · 2026-03-25 08:11:16

181

Views

Let $|a|=m$ and $|b|=n$ and $gcd(m,n)=1$. Show that $\left \langle a \right \rangle \cap \left \langle b \right \rangle = \left \{ e \right \}$.

Published on 25 Mar 2026 - 8:11

List Question

Confusing step in proof of property of cyclic group automorphisms

If $G=\langle x\rangle$ is cyclic group and order of $G$ is $40$ then how many order of $x^3$

How to arrange $p-1$ non-zero elements into $A$ groups of $B$ where $p$ is a prime number

$e^{n/e}$ estimate of the maximum order of permutation group element: proof

Intuitive understanding of $g^iH=(gH)^i$ factor groups

Exams exercise involving the permutation group $S_5$

Find the order of 5 in $\mathbb Z_{12}$

The commutator of two subgroup in a finite group

Show that, for every $x\ \epsilon \ C_{m}$, we have that $ord(f(x))$ is a divisor of d.

Why are $-1$ and $1$ generators for the Set of integers under addition?

Proof verification: For all $g\in G$, with $G$ being a group, $|a|=|g^{-1}ag|$.

What is the difference between cyclic subgroup $\left \langle a\right \rangle$ and $\left \langle a^{k} \right \rangle$?

If $f:G→ℤ_{8}$ be a group epimorphism , then what can be said about $G$?

Proof verification: Show that the intersection of two generators is a subgroup of both individual generators.

Let $|a|=m$ and $|b|=n$ and $gcd(m,n)=1$. Show that $\left \langle a \right \rangle \cap \left \langle b \right \rangle = \left \{ e \right \}$.

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