Question

A nice group isomorphism

score 72 · Answer 1 · 2013-12-07 18:26:12

72

Views

A nice group isomorphism

Published on 07 Dec 2013 - 18:26

score 601 · Answer 2 · 2013-12-09 02:29:47

601

Views

Let G be a group of order $n$, where $n$ is a positive integer relatively prime to $\varphi(n)$. Show that G is cyclic.

Published on 09 Dec 2013 - 2:29

score 2.3k · Answer 3 · 2013-12-10 11:07:34

2.3k

Views

Prove that in any group an element and its inverse have same order.

Published on 10 Dec 2013 - 11:07

score 399 · Answer 4 · 2013-12-10 12:42:20

399

Views

Cyclic subgroup of a cyclic group

Published on 10 Dec 2013 - 12:42

score 4.6k · Answer 5 · 2013-12-13 03:28:22

4.6k

Views

Finding the number of Bracelet five beads different colors

Published on 13 Dec 2013 - 3:28

score 717 · Answer 6 · 2013-12-18 14:02:33

717

Views

$(\mathbb{Z}/p^r\mathbb{Z})^{\ast}$ is a cyclic group

Published on 18 Dec 2013 - 14:02

score 6.2k · Answer 7 · 2013-12-25 09:02:34

6.2k

Views

Intuition - An inverse of a generator is a generator and powers of generators - Fraleigh p. 58 5.46

Published on 25 Dec 2013 - 9:02

score 448 · Answer 8 · 2013-12-27 09:50:49

448

Views

Intuition and Tricks - Hard Overcomplex Proof - Order of Subgroup of Cyclic Subgroup - Fraleigh p. 64 Theorem 6.14

Published on 27 Dec 2013 - 9:50

score 85 · Answer 9 · 2013-12-27 12:30:27

85

Views

A question concerning cyclic property of a group

Published on 27 Dec 2013 - 12:30

score 527 · Answer 10 · 2013-12-28 07:21:44

527

Views

Intuition and Tricks - Crafty Short Proof - Generators, Order of a Cyclic Group - Fraleigh p. 64 Theorem 6.14

Published on 28 Dec 2013 - 7:21

score 375 · Answer 11 · 2013-12-29 12:19:08

375

Views

Order of a cyclic group with a single proper subgroup of order 7

Published on 29 Dec 2013 - 12:19

score 4.1k · Answer 12 · 2013-12-30 15:09:21

4.1k

Views

Show that if $ab$ has finite order $n$, then $ba$ also has order $n$. - Fraleigh p. 47 6.46.

Published on 30 Dec 2013 - 15:09

score 1.7k · Answer 13 · 2013-12-30 16:15:00

1.7k

Views

Suppose a unique a generates a cyclic subgroup of order. Show ax = xa. - Fraleigh p. 67 6.50

Published on 30 Dec 2013 - 16:15

score 922 · Answer 14 · 2014-01-02 03:53:48

922

Views

surjective homomorphisms between cyclic groups (wrong question)

Published on 02 Jan 2014 - 3:53

score 1.2k · Answer 15 · 2026-03-29 21:55:22

1.2k

Views

Semi-direct product of groups with one of them cyclic

Published on 29 Mar 2026 - 21:55

List Question

A nice group isomorphism

Let G be a group of order $n$, where $n$ is a positive integer relatively prime to $\varphi(n)$. Show that G is cyclic.

Prove that in any group an element and its inverse have same order.

Cyclic subgroup of a cyclic group

Finding the number of Bracelet five beads different colors

$(\mathbb{Z}/p^r\mathbb{Z})^{\ast}$ is a cyclic group

Intuition - An inverse of a generator is a generator and powers of generators - Fraleigh p. 58 5.46

Intuition and Tricks - Hard Overcomplex Proof - Order of Subgroup of Cyclic Subgroup - Fraleigh p. 64 Theorem 6.14

A question concerning cyclic property of a group

Intuition and Tricks - Crafty Short Proof - Generators, Order of a Cyclic Group - Fraleigh p. 64 Theorem 6.14

Order of a cyclic group with a single proper subgroup of order 7

Show that if $ab$ has finite order $n$, then $ba$ also has order $n$. - Fraleigh p. 47 6.46.

Suppose a unique a generates a cyclic subgroup of order. Show ax = xa. - Fraleigh p. 67 6.50

surjective homomorphisms between cyclic groups (wrong question)

Semi-direct product of groups with one of them cyclic

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