Question

Show that if a group $G$ of finite order has elements of order $d,$ then $G$ has subgroups of order of every divisor of $d.$

score 801 · Answer 1 · 2020-11-29 14:40:02

801

Views

Show that if a group $G$ of finite order has elements of order $d,$ then $G$ has subgroups of order of every divisor of $d.$

Published on 29 Nov 2020 - 14:40

score 1.2k · Answer 2 · 2020-11-29 17:44:21

1.2k

Views

Which of the following statements are true about finite cyclic groups?

Published on 29 Nov 2020 - 17:44

score 313 · Answer 3 · 2020-11-30 02:40:44

313

Views

Cyclic normal subgroup of perfect group is in the center

Published on 30 Nov 2020 - 2:40

score 508 · Answer 4 · 2026-03-28 06:59:56

508

Views

Prove that the Galois group $G = Gal(x^5-2; \mathbb{Q})$ is a group metacyclic.

Published on 28 Mar 2026 - 6:59

score 374 · Answer 5 · 2026-04-03 07:17:17

374

Views

What can I say about a map multiplication?

Published on 03 Apr 2026 - 7:17

score 27 · Answer 6 · 2020-12-01 16:06:57

27

Views

For a given group to be cyclic, does the generator have to produce exactly all of its elements?

Published on 01 Dec 2020 - 16:06

score 44 · Answer 7 · 2020-12-02 16:45:12

44

Views

Help showing that a function is surjective

Published on 02 Dec 2020 - 16:45

score 127 · Answer 8 · 2026-03-26 19:02:46

127

Views

Galois group of the compositum of a non-totally-ramified and a the unramified extension of $\mathbb{Q}_p$ of prime power degree

Published on 26 Mar 2026 - 19:02

score 64 · Answer 9 · 2020-12-06 01:50:32

64

Views

Whether a group $G$ is cyclic or not.

Published on 06 Dec 2020 - 1:50

score 1.4k · Answer 10 · 2026-03-28 06:59:49

1.4k

Views

If $G/H$ is cyclic, where $H$ is a subgroup of $Z(G)$, then $G$ is abelian.

Published on 28 Mar 2026 - 6:59

score 78 · Answer 11 · 2026-04-02 22:11:37

78

Views

Show that $g(x) = 1 + x + x^2 + \dotsb + x^{n-1}$ is the generating polynomial for the $[n, 1]$ repetition code

Published on 02 Apr 2026 - 22:11

score 651 · Answer 12 · 2026-03-31 17:07:53

651

Views

Let $G$ be a group of order 77. Show that $\operatorname{Aut}(G)$ is abelian but not cyclic.

Published on 31 Mar 2026 - 17:07

score 338 · Answer 13 · 2020-12-13 00:43:28

338

Views

How to factor $x^5-1$ for binary codes

Published on 13 Dec 2020 - 0:43

score 210 · Answer 14 · 2020-12-13 19:45:51

210

Views

Order of centralizer and cyclic group over $(G,\ast)$

Published on 13 Dec 2020 - 19:45

score 57 · Answer 15 · 2020-12-15 05:30:36

57

Views

A question about cyclic groups and their isomorphisms

Published on 15 Dec 2020 - 5:30

List Question

Show that if a group $G$ of finite order has elements of order $d,$ then $G$ has subgroups of order of every divisor of $d.$

Which of the following statements are true about finite cyclic groups?

Cyclic normal subgroup of perfect group is in the center

Prove that the Galois group $G = Gal(x^5-2; \mathbb{Q})$ is a group metacyclic.

What can I say about a map multiplication?

For a given group to be cyclic, does the generator have to produce exactly all of its elements?

Help showing that a function is surjective

Galois group of the compositum of a non-totally-ramified and a the unramified extension of $\mathbb{Q}_p$ of prime power degree

Whether a group $G$ is cyclic or not.

If $G/H$ is cyclic, where $H$ is a subgroup of $Z(G)$, then $G$ is abelian.

Show that $g(x) = 1 + x + x^2 + \dotsb + x^{n-1}$ is the generating polynomial for the $[n, 1]$ repetition code

Let $G$ be a group of order 77. Show that $\operatorname{Aut}(G)$ is abelian but not cyclic.

How to factor $x^5-1$ for binary codes

Order of centralizer and cyclic group over $(G,\ast)$

A question about cyclic groups and their isomorphisms

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