Question

Proof regarding cyclic groups

score 21 · Answer 1 · 2019-10-30 15:10:26

21

Views

Proof regarding cyclic groups

Published on 30 Oct 2019 - 15:10

score 1k · Answer 2 · 2019-11-01 14:56:31

1k

Views

Nonisomorphic Groups of order $100$

Published on 01 Nov 2019 - 14:56

score 115 · Answer 3 · 2019-11-02 19:31:05

115

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Prime Order $\Rightarrow$ Cyclic $\Rightarrow$ Abelian

Published on 02 Nov 2019 - 19:31

score 519 · Answer 4 · 2019-11-04 11:42:12

519

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Find all generators for the cyclic group $\mathbb Z_9 \times \mathbb Z_4$?

Published on 04 Nov 2019 - 11:42

score 99 · Answer 5 · 2026-03-28 11:35:20

99

Views

Hypotheses for Sum of squares of degrees of irreducible representations equals order of group

Published on 28 Mar 2026 - 11:35

score 91 · Answer 6 · 2026-03-25 19:03:12

91

Views

Locally cyclic quotient and locally cyclic subgroup

Published on 25 Mar 2026 - 19:03

score 394 · Answer 7 · 2026-03-27 15:05:08

394

Views

Sylow $p$-subgroup is cyclic

Published on 27 Mar 2026 - 15:05

score 75 · Answer 8 · 2019-11-10 20:47:36

75

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Prove that $\{x \in (\Bbb Z/p\Bbb Z)^\times : x^4 = 1\}$ is a cyclic subgroup of $(\Bbb Z/p\Bbb Z)^\times$ of order four.

Published on 10 Nov 2019 - 20:47

score 134 · Answer 9 · 2019-11-11 16:02:43

134

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Generator of a group cannot be a generator of a proper subgroup

Published on 11 Nov 2019 - 16:02

score 242 · Answer 10 · 2026-03-25 18:50:18

242

Views

Show that for two cyclic groups with order $3$ and $7$, any semi-direct product are isomorphic with each other.

Published on 25 Mar 2026 - 18:50

score 792 · Answer 11 · 2019-11-11 21:04:29

792

Views

Show that G is isomorphic to C4

Published on 11 Nov 2019 - 21:04

score 541 · Answer 12 · 2026-03-29 11:50:04

541

Views

Assume $N \triangleleft G$ Prove that if $[G:H]$ is a prime, then $G/N$ is cyclic. prove or disprove the converse of the first statement.

Published on 29 Mar 2026 - 11:50

score 157 · Answer 13 · 2019-11-14 07:48:16

157

Views

Why are the elements of the Cyclic Group with Generator $\langle 3 \rangle$ in $\mathbb{Z_{15}}$ {0, 3, 6, 9, 12} and not {1, 3, 9}

Published on 14 Nov 2019 - 7:48

score 62 · Answer 14 · 2019-11-17 20:55:07

62

Views

All proper subgroups cyclic

Published on 17 Nov 2019 - 20:55

score 261 · Answer 15 · 2026-03-29 04:54:58

261

Views

Prove or disprove: The automorphism group of a finite cyclic group must be cyclic.

Published on 29 Mar 2026 - 4:54

List Question

Proof regarding cyclic groups

Nonisomorphic Groups of order $100$

Prime Order $\Rightarrow$ Cyclic $\Rightarrow$ Abelian

Find all generators for the cyclic group $\mathbb Z_9 \times \mathbb Z_4$?

Hypotheses for Sum of squares of degrees of irreducible representations equals order of group

Locally cyclic quotient and locally cyclic subgroup

Sylow $p$-subgroup is cyclic

Prove that $\{x \in (\Bbb Z/p\Bbb Z)^\times : x^4 = 1\}$ is a cyclic subgroup of $(\Bbb Z/p\Bbb Z)^\times$ of order four.

Generator of a group cannot be a generator of a proper subgroup

Show that for two cyclic groups with order $3$ and $7$, any semi-direct product are isomorphic with each other.

Show that G is isomorphic to C4

Assume $N \triangleleft G$ Prove that if $[G:H]$ is a prime, then $G/N$ is cyclic. prove or disprove the converse of the first statement.

Why are the elements of the Cyclic Group with Generator $\langle 3 \rangle$ in $\mathbb{Z_{15}}$ {0, 3, 6, 9, 12} and not {1, 3, 9}

All proper subgroups cyclic

Prove or disprove: The automorphism group of a finite cyclic group must be cyclic.

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