Question

Classify $\mathbb{Z}_{108}$ up to an isomorphism

score 290 · Answer 1 · 2026-03-26 12:13:36

290

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Classify $\mathbb{Z}_{108}$ up to an isomorphism

Published on 26 Mar 2026 - 12:13

score 97 · Answer 2 · 2026-03-26 08:14:51

97

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Construct a non-trivial homomorphism: $\mathbb{Z}_2 \times \mathbb{Z}_4 \longrightarrow \mathbb{Z}_8$

Published on 26 Mar 2026 - 8:14

score 493 · Answer 3 · 2018-12-17 21:18:11

493

Views

Number of roots of a quadratic polynomial with coefficients in ring $\mathbb{Z_{18}}$

Published on 17 Dec 2018 - 21:18

score 67 · Answer 4 · 2018-12-18 02:30:16

67

Views

If $\mathbb{Z}_m \times \mathbb{Z}_n \cong \mathbb{Z}_{m'} \times \mathbb{Z}_{n'}$ with $m|n$ and $m'|n'$, then does $m=m'$ and $n=n'$?

Published on 18 Dec 2018 - 2:30

score 68 · Answer 5 · 2026-03-26 09:13:30

68

Views

Finite abelian group $G$, with $N \triangleleft G$ cyclic and $G/N$ cyclic

Published on 26 Mar 2026 - 9:13

score 182 · Answer 6 · 2018-12-21 18:17:44

182

Views

About every subgroup of $ ( \mathbb{Z} , + ) $ being cyclic.

Published on 21 Dec 2018 - 18:17

score 92 · Answer 7 · 2026-03-25 08:14:04

92

Views

Show that any finite nilpotent group of square free order is cyclic.

Published on 25 Mar 2026 - 8:14

score 327 · Answer 8 · 2018-12-24 04:52:59

327

Views

Let $\left\{ H_i | i \in I\right\}$ be a family of subgroups of G. State and prove a condition which makes $\cup_{i \in I} H_{i}$ a subgroup of $G$

Published on 24 Dec 2018 - 4:52

score 397 · Answer 9 · 2026-03-26 06:09:37

397

Views

Fundamental Group Contains Infinite Cyclic Subgroup

Published on 26 Mar 2026 - 6:09

score 156 · Answer 10 · 2018-12-26 20:37:26

156

Views

Exercise 4.11 Allufi

Published on 26 Dec 2018 - 20:37

score 256 · Answer 11 · 2026-03-26 09:41:53

256

Views

About the Proof for "the Order of a Permutation $\sigma$ is the $lcm$ of the Orders of its Disjoint Cycles."

Published on 26 Mar 2026 - 9:41

score 1.8k · Answer 12 · 2026-03-26 08:15:00

1.8k

Views

If $\varphi$ is a homomorphism, $\text{ord}(\varphi(a))$ divides $\text{ord}(a)$

Published on 26 Mar 2026 - 8:15

score 108 · Answer 13 · 2026-03-26 11:17:40

108

Views

There exists an element of order $5$ in $G$

Published on 26 Mar 2026 - 11:17

score 50 · Answer 14 · 2018-12-29 18:27:31

50

Views

Prove that two groups act in the same way

Published on 29 Dec 2018 - 18:27

score 1.8k · Answer 15 · 2018-12-31 09:27:20

1.8k

Views

Regarding $|\textrm{G}| = 65$ $\Rightarrow$ $\textrm{G}$ is cyclic.

Published on 31 Dec 2018 - 9:27

List Question

Classify $\mathbb{Z}_{108}$ up to an isomorphism

Construct a non-trivial homomorphism: $\mathbb{Z}_2 \times \mathbb{Z}_4 \longrightarrow \mathbb{Z}_8$

Number of roots of a quadratic polynomial with coefficients in ring $\mathbb{Z_{18}}$

If $\mathbb{Z}_m \times \mathbb{Z}_n \cong \mathbb{Z}_{m'} \times \mathbb{Z}_{n'}$ with $m|n$ and $m'|n'$, then does $m=m'$ and $n=n'$?

Finite abelian group $G$, with $N \triangleleft G$ cyclic and $G/N$ cyclic

About every subgroup of $ ( \mathbb{Z} , + ) $ being cyclic.

Show that any finite nilpotent group of square free order is cyclic.

Let $\left\{ H_i | i \in I\right\}$ be a family of subgroups of G. State and prove a condition which makes $\cup_{i \in I} H_{i}$ a subgroup of $G$

Fundamental Group Contains Infinite Cyclic Subgroup

Exercise 4.11 Allufi

About the Proof for "the Order of a Permutation $\sigma$ is the $lcm$ of the Orders of its Disjoint Cycles."

If $\varphi$ is a homomorphism, $\text{ord}(\varphi(a))$ divides $\text{ord}(a)$

There exists an element of order $5$ in $G$

Prove that two groups act in the same way

Regarding $|\textrm{G}| = 65$ $\Rightarrow$ $\textrm{G}$ is cyclic.

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