Question

Find a product of cyclic groups isomorphic to $(\mathbb{Z}_{12} × \mathbb{Z}_{12}) /\langle(2, 6)\rangle$.

score 382 · Answer 1 · 2017-07-07 05:48:39

382

Views

Find a product of cyclic groups isomorphic to $(\mathbb{Z}_{12} × \mathbb{Z}_{12}) /\langle(2, 6)\rangle$.

Published on 07 Jul 2017 - 5:48

score 4k · Answer 2 · 2017-07-07 12:12:35

4k

Views

Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic

Published on 07 Jul 2017 - 12:12

score 1.5k · Answer 3 · 2017-07-09 16:22:14

1.5k

Views

How many isomorphisms are there between two cyclic groups of order $n > 0$?

Published on 09 Jul 2017 - 16:22

score 904 · Answer 4 · 2017-07-10 19:31:58

904

Views

Calculations of elements of S5 in cycle notation

Published on 10 Jul 2017 - 19:31

score 212 · Answer 5 · 2017-07-10 20:37:16

212

Views

Cycle Notation Calculations of S6

Published on 10 Jul 2017 - 20:37

score 55 · Answer 6 · 2017-07-11 06:56:39

55

Views

Calculation of elements of $S_6$ in cycle notation, (indice types)

Published on 11 Jul 2017 - 6:56

score 1.4k · Answer 7 · 2026-04-02 01:48:57

1.4k

Views

The homomorphism on a cyclic group is the action of the homomorphism's action on the generator of the cyclic group

Published on 02 Apr 2026 - 1:48

score 200 · Answer 8 · 2017-07-18 04:07:25

200

Views

Find the order of cyclic group.

Published on 18 Jul 2017 - 4:07

score 339 · Answer 9 · 2017-07-26 03:38:56

339

Views

Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.

Published on 26 Jul 2017 - 3:38

score 375 · Answer 10 · 2026-03-28 08:09:27

375

Views

Help with understanding proof: every group of order 6 is cclic or dihedral.

Published on 28 Mar 2026 - 8:09

score 50 · Answer 11 · 2017-08-04 03:15:38

50

Views

Suppose $G$ be a finite group, $a \in G$ has finite order, then check whether the formula true or false?

Published on 04 Aug 2017 - 3:15

score 61 · Answer 12 · 2026-02-23 06:01:35

61

Views

How could I describe homomorphisms from $C_m \rightarrow C_n$?

Published on 23 Feb 2026 - 6:01

score 1.5k · Answer 13 · 2017-08-14 02:18:50

1.5k

Views

Identity elements in a cyclic group

Published on 14 Aug 2017 - 2:18

score 310 · Answer 14 · 2026-03-26 06:27:18

310

Views

Extensions to a homomorphism

Published on 26 Mar 2026 - 6:27

score 224 · Answer 15 · 2017-08-18 18:42:21

224

Views

Prove that $S_k(p)= \begin{cases} -1, & \text{if $(p-1)\mid k$ } \\ 0, & \text{otherwise} \end{cases}$ in $\Bbb Z_p$

Published on 18 Aug 2017 - 18:42

List Question

Find a product of cyclic groups isomorphic to $(\mathbb{Z}_{12} × \mathbb{Z}_{12}) /\langle(2, 6)\rangle$.

Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic

How many isomorphisms are there between two cyclic groups of order $n > 0$?

Calculations of elements of S5 in cycle notation

Cycle Notation Calculations of S6

Calculation of elements of $S_6$ in cycle notation, (indice types)

The homomorphism on a cyclic group is the action of the homomorphism's action on the generator of the cyclic group

Find the order of cyclic group.

Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.

Help with understanding proof: every group of order 6 is cclic or dihedral.

Suppose $G$ be a finite group, $a \in G$ has finite order, then check whether the formula true or false?

How could I describe homomorphisms from $C_m \rightarrow C_n$?

Identity elements in a cyclic group

Extensions to a homomorphism

Prove that $S_k(p)= \begin{cases} -1, & \text{if $(p-1)\mid k$ } \\ 0, & \text{otherwise} \end{cases}$ in $\Bbb Z_p$

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