Question

Cyclic group with special property

score 90 · Answer 1 · 2018-10-20 12:06:06

90

Views

Cyclic group with special property

Published on 20 Oct 2018 - 12:06

score 151 · Answer 2 · 2018-10-22 20:46:45

151

Views

Is it true that every cyclic group of order $n$ contains exactly the same number of subgroups as the number of divisors of $n$?

Published on 22 Oct 2018 - 20:46

score 1k · Answer 3 · 2018-10-24 04:27:10

1k

Views

how to show that a group of order $p^k$ has subgroups of order $p^i$

Published on 24 Oct 2018 - 4:27

score 67 · Answer 4 · 2018-10-28 16:33:16

67

Views

Problem regarding proving a field to be finite.

Published on 28 Oct 2018 - 16:33

score 134 · Answer 5 · 2018-10-30 14:06:59

134

Views

Do two elements of order $p$ generate a group of order $p^2m$?

Published on 30 Oct 2018 - 14:06

score 198 · Answer 6 · 2018-10-30 14:28:13

198

Views

$\alpha \nmid n \Rightarrow \alpha$ is a generator of group $G$

Published on 30 Oct 2018 - 14:28

score 56 · Answer 7 · 2026-03-25 11:16:23

56

Views

Are two lifts of a generator of a cyclic quotient conjugated?

Published on 25 Mar 2026 - 11:16

score 202 · Answer 8 · 2018-11-01 17:44:52

202

Views

Finite field where each subgroup of the multiplicative group of nonzero elements of the field, together with $0$, forms a field.

Published on 01 Nov 2018 - 17:44

score 53 · Answer 9 · 2026-03-25 23:42:20

53

Views

for any integer $n\ge2$, consider the group ${\bf Z}_{p^n}\oplus{\bf Z}_p$. Determine the number of cyclic subgroups of order $p$

Published on 25 Mar 2026 - 23:42

score 573 · Answer 10 · 2018-11-05 05:21:49

573

Views

Homomorphisms from $\mathbb{Z}/48\mathbb{Z}$ into $\mathbb{Z}/36\mathbb{Z}$

Published on 05 Nov 2018 - 5:21

score 155 · Answer 11 · 2026-03-25 16:00:26

155

Views

Given that $G$ is cyclic then $G/N$ is cyclic.

Published on 25 Mar 2026 - 16:00

score 1.1k · Answer 12 · 2026-03-25 15:52:35

1.1k

Views

Deduce that $\mbox{Aut}(\mathbb{Z}/n\mathbb{Z})$ is isomorphic to $(\mathbb{Z}/n\mathbb{Z})^*$ (a group under multiplication)

Published on 25 Mar 2026 - 15:52

score 206 · Answer 13 · 2026-03-25 12:50:47

206

Views

Lift of a generator of a non-trivial quotient of a cyclic group with prime power order must be a generator of the whole group

Published on 25 Mar 2026 - 12:50

score 124 · Answer 14 · 2026-03-26 05:55:59

124

Views

Are groups of order $p^2$ abelian, $p$ prime?

Published on 26 Mar 2026 - 5:55

score 224 · Answer 15 · 2018-11-09 01:13:07

224

Views

Group Theory greatest common divisor and order

Published on 09 Nov 2018 - 1:13

List Question

Cyclic group with special property

Is it true that every cyclic group of order $n$ contains exactly the same number of subgroups as the number of divisors of $n$?

how to show that a group of order $p^k$ has subgroups of order $p^i$

Problem regarding proving a field to be finite.

Do two elements of order $p$ generate a group of order $p^2m$?

$\alpha \nmid n \Rightarrow \alpha$ is a generator of group $G$

Are two lifts of a generator of a cyclic quotient conjugated?

Finite field where each subgroup of the multiplicative group of nonzero elements of the field, together with $0$, forms a field.

for any integer $n\ge2$, consider the group ${\bf Z}_{p^n}\oplus{\bf Z}_p$. Determine the number of cyclic subgroups of order $p$

Homomorphisms from $\mathbb{Z}/48\mathbb{Z}$ into $\mathbb{Z}/36\mathbb{Z}$

Given that $G$ is cyclic then $G/N$ is cyclic.

Deduce that $\mbox{Aut}(\mathbb{Z}/n\mathbb{Z})$ is isomorphic to $(\mathbb{Z}/n\mathbb{Z})^*$ (a group under multiplication)

Lift of a generator of a non-trivial quotient of a cyclic group with prime power order must be a generator of the whole group

Are groups of order $p^2$ abelian, $p$ prime?

Group Theory greatest common divisor and order

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