Question

Find all subgroups of $\mathbb{Z}_2\oplus\mathbb{Z}_4$ of order $4$

score 1k · Answer 1 · 2019-12-09 03:35:46

1k

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Find all subgroups of $\mathbb{Z}_2\oplus\mathbb{Z}_4$ of order $4$

Published on 09 Dec 2019 - 3:35

score 49 · Answer 2 · 2026-03-26 03:13:31

49

Views

$G = S_7$, $a=(2,5,7)$, $b=(5,7)(4,3,1,6)$, $H = \langle a, b \rangle$, and let $K=\langle b \rangle$. Find a cyclic subgroup of $H$ of order 3 and 6

Published on 26 Mar 2026 - 3:13

score 230 · Answer 3 · 2026-03-28 00:49:19

230

Views

For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?

Published on 28 Mar 2026 - 0:49

score 288 · Answer 4 · 2026-03-28 00:47:42

288

Views

Cyclic group and homomorphism

Published on 28 Mar 2026 - 0:47

score 205 · Answer 5 · 2019-12-14 21:48:46

205

Views

Maximal Order of Elements in Finite Abelian Group

Published on 14 Dec 2019 - 21:48

score 1.9k · Answer 6 · 2019-12-16 06:20:58

1.9k

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Prove that $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not cyclic

Published on 16 Dec 2019 - 6:20

score 157 · Answer 7 · 2019-12-16 12:51:13

157

Views

Prove that $\mathbb{Q}\times \mathbb{Z_2}$ not isomorphic to $\mathbb{Q}$

Published on 16 Dec 2019 - 12:51

score 354 · Answer 8 · 2019-12-16 13:45:42

354

Views

A finite abelian group in which each element has order 1 or $p$, $p$ prime, is an elementary abelian group

Published on 16 Dec 2019 - 13:45

score 99 · Answer 9 · 2019-12-19 08:58:07

99

Views

$|x|=7$,$|y|=3$ then $|\langle x,y \rangle |=21$

Published on 19 Dec 2019 - 8:58

score 865 · Answer 10 · 2019-12-19 22:51:32

865

Views

Is every Abelian group isomorphic to the external direct product of two cyclic groups?

Published on 19 Dec 2019 - 22:51

score 452 · Answer 11 · 2019-12-23 02:38:57

452

Views

Finite abelian group A cyclic iff for every $n\in \mathbb{N}$, $|\{a\in A \mid a^n = 1\}| \leq n$

Published on 23 Dec 2019 - 2:38

score 38 · Answer 12 · 2019-12-24 12:21:09

38

Views

How many generators of the group $U(n)$ are there?

Published on 24 Dec 2019 - 12:21

score 60 · Answer 13 · 2019-12-25 03:19:09

60

Views

Сyclic subgroup

Published on 25 Dec 2019 - 3:19

score 58 · Answer 14 · 2026-03-25 17:20:54

58

Views

Show that $\langle x,y,z \rangle$ has order $42$ for $x,y,z$ with given properties

Published on 25 Mar 2026 - 17:20

score 230 · Answer 15 · 2026-03-26 09:26:57

230

Views

Prove or disprove: For every integer $n$, the quotient group of $\Bbb Z/n\Bbb Z$ modulo any subgroup is cyclic.

Published on 26 Mar 2026 - 9:26

List Question

Find all subgroups of $\mathbb{Z}_2\oplus\mathbb{Z}_4$ of order $4$

$G = S_7$, $a=(2,5,7)$, $b=(5,7)(4,3,1,6)$, $H = \langle a, b \rangle$, and let $K=\langle b \rangle$. Find a cyclic subgroup of $H$ of order 3 and 6

For which $n$ and $k$ are there nontrivial homomorphisms from $S_n$ to $\mathbb{Z}/k\mathbb{Z}$?

Cyclic group and homomorphism

Maximal Order of Elements in Finite Abelian Group

Prove that $\mathbb{Z}_2 \times \mathbb{Z}_2$ is not cyclic

Prove that $\mathbb{Q}\times \mathbb{Z_2}$ not isomorphic to $\mathbb{Q}$

A finite abelian group in which each element has order 1 or $p$, $p$ prime, is an elementary abelian group

$|x|=7$,$|y|=3$ then $|\langle x,y \rangle |=21$

Is every Abelian group isomorphic to the external direct product of two cyclic groups?

Finite abelian group A cyclic iff for every $n\in \mathbb{N}$, $|\{a\in A \mid a^n = 1\}| \leq n$

How many generators of the group $U(n)$ are there?

Сyclic subgroup

Show that $\langle x,y,z \rangle$ has order $42$ for $x,y,z$ with given properties

Prove or disprove: For every integer $n$, the quotient group of $\Bbb Z/n\Bbb Z$ modulo any subgroup is cyclic.

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