Question

$a$ and $b$ are elements of the group $G$, then if $a \in \langle b \rangle$, then $\langle a\rangle \subseteq \langle b\rangle$

score 141 · Answer 1 · 2023-11-25 18:55:07

141

Views

$a$ and $b$ are elements of the group $G$, then if $a \in \langle b \rangle$, then $\langle a\rangle \subseteq \langle b\rangle$

Published on 25 Nov 2023 - 18:55

score 398 · Answer 2 · 2023-11-27 11:14:39

398

Views

Is only one generator enough to find other generators?

Published on 27 Nov 2023 - 11:14

score 42 · Answer 3 · 2026-03-29 18:48:58

42

Views

Isomorphisms between cyclic groups

Published on 29 Mar 2026 - 18:48

score 49 · Answer 4 · 2023-12-09 22:10:46

49

Views

Calculate product of disjoint cycles

Published on 09 Dec 2023 - 22:10

score 140 · Answer 5 · 2023-12-13 04:15:20

140

Views

Is this a valid proof? Group Theory

Published on 13 Dec 2023 - 4:15

score 115 · Answer 6 · 2023-12-17 16:33:13

115

Views

How can I see that $o(G) = p^n$ without using the fundamental theorem of finitely generated abelian groups?

Published on 17 Dec 2023 - 16:33

score 72 · Answer 7 · 2023-12-18 08:00:26

72

Views

Confusion about the proof of $\langle a^k\rangle=\langle a^{(n,k)}\rangle$

Published on 18 Dec 2023 - 8:00

score 74 · Answer 8 · 2023-12-21 06:46:41

74

Views

A cyclic group of order $n$ has a unique subgroup of order $d$ for each $d\mid n$

Published on 21 Dec 2023 - 6:46

score 185 · Answer 9 · 2026-03-26 03:00:23

185

Views

Non-constructiveness and finite mathematics

Published on 26 Mar 2026 - 3:00

score 40 · Answer 10 · 2026-03-28 23:59:59

40

Views

Vinogradov's proof that $U_{p^{\alpha}}$ is cyclic. How to prove $p^{r-1} (p-1) \mid \delta$ for $1 \leq r \leq \alpha$

Published on 28 Mar 2026 - 23:59

score 44 · Answer 11 · 2023-12-23 06:04:15

44

Views

Every automorphism of $Z_n$ is equal to some $\sigma_a$

Published on 23 Dec 2023 - 6:04

score 46 · Answer 12 · 2023-12-24 14:48:54

46

Views

What should I type in Archive.org search bar to find books covering proof of $U_{p^α}$ is cyclic (where $p$ is an odd prime)?

Published on 24 Dec 2023 - 14:48

score 52 · Answer 13 · 2023-12-25 15:36:49

52

Views

Isomorphism of cyclic groups $U(p)$ and $\mathbb{Z}_{p-1}$

Published on 25 Dec 2023 - 15:36

score 137 · Answer 14 · 2026-03-30 15:36:14

137

Views

What is the isomorphism class of the kernel of a homomorphism of cyclic groups?

Published on 30 Mar 2026 - 15:36

score 23 · Answer 15 · 2026-03-24 23:09:32

23

Views

Why is pointwise stabilizer of a reflecting hyperplane a cyclic group?

Published on 24 Mar 2026 - 23:09

List Question

$a$ and $b$ are elements of the group $G$, then if $a \in \langle b \rangle$, then $\langle a\rangle \subseteq \langle b\rangle$

Is only one generator enough to find other generators?

Isomorphisms between cyclic groups

Calculate product of disjoint cycles

Is this a valid proof? Group Theory

How can I see that $o(G) = p^n$ without using the fundamental theorem of finitely generated abelian groups?

Confusion about the proof of $\langle a^k\rangle=\langle a^{(n,k)}\rangle$

A cyclic group of order $n$ has a unique subgroup of order $d$ for each $d\mid n$

Non-constructiveness and finite mathematics

Vinogradov's proof that $U_{p^{\alpha}}$ is cyclic. How to prove $p^{r-1} (p-1) \mid \delta$ for $1 \leq r \leq \alpha$

Every automorphism of $Z_n$ is equal to some $\sigma_a$

What should I type in Archive.org search bar to find books covering proof of $U_{p^α}$ is cyclic (where $p$ is an odd prime)?

Isomorphism of cyclic groups $U(p)$ and $\mathbb{Z}_{p-1}$

What is the isomorphism class of the kernel of a homomorphism of cyclic groups?

Why is pointwise stabilizer of a reflecting hyperplane a cyclic group?

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