Question

Show the set of positive rationals under multiplication is not cyclic

score 2.2k · Answer 1 · 2016-10-01 06:32:13

2.2k

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Show the set of positive rationals under multiplication is not cyclic

Published on 01 Oct 2016 - 6:32

score 1.3k · Answer 2 · 2026-03-25 06:13:08

1.3k

Views

Understanding the wreath product of $\mathbb Z_2$ by $\mathbb Z_2$ and of $\mathbb Z_2$ by $\mathbb Z_3$

Published on 25 Mar 2026 - 6:13

score 64 · Answer 3 · 2026-03-25 13:44:57

64

Views

What is the largest (if any) multiplicative modulo group with all prime elements?

Published on 25 Mar 2026 - 13:44

score 1.2k · Answer 4 · 2016-10-04 01:48:12

1.2k

Views

Prove that $\mathbb{Z}_{p}$, where $p$ is a prime number, has no nontrivial subgroups

Published on 04 Oct 2016 - 1:48

score 50 · Answer 5 · 2016-10-04 04:19:43

50

Views

Clever way of showing the map sending to prime power is outer automorphism

Published on 04 Oct 2016 - 4:19

score 47 · Answer 6 · 2016-10-04 08:59:07

47

Views

Criterion for a subset of $\mathbb{Z}_p$ be a cyclyc group

Published on 04 Oct 2016 - 8:59

score 64 · Answer 7 · 2016-10-04 18:56:00

64

Views

A confusion on a Theorem

Published on 04 Oct 2016 - 18:56

score 134 · Answer 8 · 2016-10-07 03:12:49

134

Views

Prove that all subgroup of a cyclic group generated by $a$ is of the form $\langle a^k\rangle$ where $k|o(G)$

Published on 07 Oct 2016 - 3:12

score 4.5k · Answer 9 · 2016-10-07 09:18:31

4.5k

Views

If every cyclic subgroup of a group G be normal in G, prove that every subgroup of G is normal in G.

Published on 07 Oct 2016 - 9:18

score 555 · Answer 10 · 2016-10-10 01:39:08

555

Views

Is there any elegent way to formally prove that the ring $\mathbb Z/(8)$ cannot be decomposed to a product of rings?

Published on 10 Oct 2016 - 1:39

score 345 · Answer 11 · 2016-10-10 08:48:44

345

Views

Infinite Group with exactly one subgroup

Published on 10 Oct 2016 - 8:48

score 233 · Answer 12 · 2026-03-30 03:19:15

233

Views

Consider the group $s_3$ of example 8.7

Published on 30 Mar 2026 - 3:19

score 45 · Answer 13 · 2016-10-14 14:52:48

45

Views

Euler function: Show that if $d|n, |\{x \in C: ord(x) = d\}| = \phi(d)$ where C is a cyclic group

Published on 14 Oct 2016 - 14:52

score 451 · Answer 14 · 2026-03-27 18:48:37

451

Views

Need solution verification: Describe all $2$-generated subgroups of $\mathbb{Q}$

Published on 27 Mar 2026 - 18:48

score 291 · Answer 15 · 2016-10-16 19:36:09

291

Views

Prove that if $[2]$ is a generator for $\mathbb{Z_{9}^{\times}}$, then $[5]$ is as well.

Published on 16 Oct 2016 - 19:36

List Question

Show the set of positive rationals under multiplication is not cyclic

Understanding the wreath product of $\mathbb Z_2$ by $\mathbb Z_2$ and of $\mathbb Z_2$ by $\mathbb Z_3$

What is the largest (if any) multiplicative modulo group with all prime elements?

Prove that $\mathbb{Z}_{p}$, where $p$ is a prime number, has no nontrivial subgroups

Clever way of showing the map sending to prime power is outer automorphism

Criterion for a subset of $\mathbb{Z}_p$ be a cyclyc group

A confusion on a Theorem

Prove that all subgroup of a cyclic group generated by $a$ is of the form $\langle a^k\rangle$ where $k|o(G)$

If every cyclic subgroup of a group G be normal in G, prove that every subgroup of G is normal in G.

Is there any elegent way to formally prove that the ring $\mathbb Z/(8)$ cannot be decomposed to a product of rings?

Infinite Group with exactly one subgroup

Consider the group $s_3$ of example 8.7

Euler function: Show that if $d|n, |\{x \in C: ord(x) = d\}| = \phi(d)$ where C is a cyclic group

Need solution verification: Describe all $2$-generated subgroups of $\mathbb{Q}$

Prove that if $[2]$ is a generator for $\mathbb{Z_{9}^{\times}}$, then $[5]$ is as well.

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