Question

When is the one parameter group of diffeomorphisms isomorphic to the circle group $T$?

score 700 · Answer 1 · 2016-11-14 18:57:51

700

Views

When is the one parameter group of diffeomorphisms isomorphic to the circle group $T$?

Published on 14 Nov 2016 - 18:57

score 1.8k · Answer 2 · 2016-11-15 10:16:04

1.8k

Views

Show that any automorphism of $\mathbb{Z}_n$ is equal to multiplication by $f(1)$ mod $n$.

Published on 15 Nov 2016 - 10:16

score 60 · Answer 3 · 2016-11-15 13:08:00

60

Views

Prove that $\mathbb{R}^\ast \cong \mathbb{R}_{>0} \times \mathbb{Z}_2$

Published on 15 Nov 2016 - 13:08

score 441 · Answer 4 · 2026-03-26 22:58:45

441

Views

Connecting homomorphism between cohomology groups

Published on 26 Mar 2026 - 22:58

score 1.2k · Answer 5 · 2016-11-18 00:16:11

1.2k

Views

how to show that the groups are not isomorphic

Published on 18 Nov 2016 - 0:16

score 2.7k · Answer 6 · 2016-11-18 10:26:22

2.7k

Views

If two finite groups have the same number of elements of the same order, does this necessarily imply they are isomorphic?

Published on 18 Nov 2016 - 10:26

score 81 · Answer 7 · 2016-11-20 03:52:38

81

Views

Isomorphism between $\mathbb Q \times C_2$ and $\mathbb Q^*$

Published on 20 Nov 2016 - 3:52

score 83 · Answer 8 · 2016-11-21 13:06:53

83

Views

True/false: If two finite abelian groups of the same order have equal sum of element orders, then they are isomorphic?

Published on 21 Nov 2016 - 13:06

score 3.7k · Answer 9 · 2016-11-21 20:42:13

3.7k

Views

Is it true that an isomorphism maps elements of the same order to each other?

Published on 21 Nov 2016 - 20:42

score 1.1k · Answer 10 · 2016-11-23 16:50:15

1.1k

Views

Showing that a group is isomorphic to a subgroup of the direct product of two factor groups

Published on 23 Nov 2016 - 16:50

score 234 · Answer 11 · 2016-11-25 01:14:36

234

Views

Finding the image of a ring homomorphism

Published on 25 Nov 2016 - 1:14

score 457 · Answer 12 · 2026-03-31 07:48:47

457

Views

Are characteristic subgroups "unique" within the containing group?

Published on 31 Mar 2026 - 7:48

score 273 · Answer 13 · 2026-03-26 22:58:43

273

Views

To which group is the subgroup isomorphic?

Published on 26 Mar 2026 - 22:58

score 986 · Answer 14 · 2016-11-26 23:27:42

986

Views

Let $\phi : G → K$ be an isomorphism of groups. Prove that $G$ is abelian if and only if $K$ is abelian.

Published on 26 Nov 2016 - 23:27

score 477 · Answer 15 · 2026-03-26 19:19:30

477

Views

Showing $\Bbb Z_2 + \Bbb Z_3$ is isomorphic to $\Bbb Z_6$.

Published on 26 Mar 2026 - 19:19

List Question

When is the one parameter group of diffeomorphisms isomorphic to the circle group $T$?

Show that any automorphism of $\mathbb{Z}_n$ is equal to multiplication by $f(1)$ mod $n$.

Prove that $\mathbb{R}^\ast \cong \mathbb{R}_{>0} \times \mathbb{Z}_2$

Connecting homomorphism between cohomology groups

how to show that the groups are not isomorphic

If two finite groups have the same number of elements of the same order, does this necessarily imply they are isomorphic?

Isomorphism between $\mathbb Q \times C_2$ and $\mathbb Q^*$

True/false: If two finite abelian groups of the same order have equal sum of element orders, then they are isomorphic?

Is it true that an isomorphism maps elements of the same order to each other?

Showing that a group is isomorphic to a subgroup of the direct product of two factor groups

Finding the image of a ring homomorphism

Are characteristic subgroups "unique" within the containing group?

To which group is the subgroup isomorphic?

Let $\phi : G → K$ be an isomorphism of groups. Prove that $G$ is abelian if and only if $K$ is abelian.

Showing $\Bbb Z_2 + \Bbb Z_3$ is isomorphic to $\Bbb Z_6$.

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