Question

How to calculate the automorphisms group of nonzero rational number multiplicative group?

score 214 · Answer 1 · 2018-03-11 15:00:11

How to calculate the automorphisms group of nonzero rational number multiplicative group?

Published on 11 Mar 2018 - 15:00

score 99 · Answer 2 · 2018-03-12 00:42:53

Let $f:\Bbb{R^\times}\to\Bbb{R^\times}$ be an isomorphism. Show that $f$ takes $\Bbb R^{>0}$ to $\Bbb R^{>0}$, and $\Bbb R^{<0}$ to $\Bbb R^{<0}$.

score 2.5k · Answer 3 · 2026-03-25 09:26:23

2.5k

Views

Is $\Bbb R/\Bbb Z$ isomorphic to $\Bbb R/2\Bbb Z$?

Published on 25 Mar 2026 - 9:26

score 436 · Answer 4 · 2018-03-12 22:40:52

436

Views

Isomorphism between direct products

Published on 12 Mar 2018 - 22:40

score 99 · Answer 5 · 2018-03-13 13:58:41

99

Views

Is $ \{ x+xi \ | \ x \in R \}$ isomorphic to a straight line through the origin in $R^2$?

Published on 13 Mar 2018 - 13:58

score 89 · Answer 6 · 2026-03-27 13:18:59

89

Views

Are the groups $\mathbb{C}$ and $\mathbb{R}^2$ isomorphic under addition?

Published on 27 Mar 2026 - 13:18

score 586 · Answer 7 · 2026-03-25 09:28:20

586

Views

If group homomorphisms preserve inverses, why aren't they just isomorphisms?

Published on 25 Mar 2026 - 9:28

score 84 · Answer 8 · 2018-03-14 04:31:46

84

Views

Prove that $\mathbb{R}^\times\times\mathbb{R}^\times\ncong\mathbb{C}^\times$

Published on 14 Mar 2018 - 4:31

score 944 · Answer 9 · 2026-03-26 19:01:49

944

Views

Verify that the following is an isomorphism $T$:$P_1$ → $R^2; T[p(x)]=[p(0),p(1)]$

Published on 26 Mar 2026 - 19:01

score 2.1k · Answer 10 · 2018-03-20 02:03:14

2.1k

Views

In general, what techniques can be used to show that 2 groups are not isomorphic?

Published on 20 Mar 2018 - 2:03

score 34 · Answer 11 · 2018-03-21 20:21:09

34

Views

Show that $f_{|\,f[G]}$ is an isomorphism where $f(g)=g^2$ (no elements of order 4)

Published on 21 Mar 2018 - 20:21

score 1.5k · Answer 12 · 2026-03-25 19:11:43

1.5k

Views

Elliptic curve group of $y^2 = x^3 + 2x + 3$ over $\mathbb{F}_5$

Published on 25 Mar 2026 - 19:11

score 41 · Answer 13 · 2026-03-25 09:37:01

41

Views

$\mathbb{Z}^k/A\mathbb{Z}^k \cong\mathbb{Z}^k/A'\mathbb{Z}^k$

Published on 25 Mar 2026 - 9:37

score 326 · Answer 14 · 2018-03-24 19:37:19

326

Views

Show that $\mathbb{Z}$ is isomorphic to $n\mathbb{Z}$.

Published on 24 Mar 2018 - 19:37

score 594 · Answer 15 · 2018-03-27 00:29:50

594

Views

Show that $S$ is the internal direct product isomorphic to $\Bbb{Z}\times \Bbb{Z}$.

Published on 27 Mar 2018 - 0:29

List Question

How to calculate the automorphisms group of nonzero rational number multiplicative group?

Let $f:\Bbb{R^\times}\to\Bbb{R^\times}$ be an isomorphism. Show that $f$ takes $\Bbb R^{>0}$ to $\Bbb R^{>0}$, and $\Bbb R^{<0}$ to $\Bbb R^{<0}$.

Is $\Bbb R/\Bbb Z$ isomorphic to $\Bbb R/2\Bbb Z$?

Isomorphism between direct products

Is $ \{ x+xi \ | \ x \in R \}$ isomorphic to a straight line through the origin in $R^2$?

Are the groups $\mathbb{C}$ and $\mathbb{R}^2$ isomorphic under addition?

If group homomorphisms preserve inverses, why aren't they just isomorphisms?

Prove that $\mathbb{R}^\times\times\mathbb{R}^\times\ncong\mathbb{C}^\times$

Verify that the following is an isomorphism $T$:$P_1$ → $R^2; T[p(x)]=[p(0),p(1)]$

In general, what techniques can be used to show that 2 groups are not isomorphic?

Show that $f_{|\,f[G]}$ is an isomorphism where $f(g)=g^2$ (no elements of order 4)

Elliptic curve group of $y^2 = x^3 + 2x + 3$ over $\mathbb{F}_5$

$\mathbb{Z}^k/A\mathbb{Z}^k \cong\mathbb{Z}^k/A'\mathbb{Z}^k$

Show that $\mathbb{Z}$ is isomorphic to $n\mathbb{Z}$.

Show that $S$ is the internal direct product isomorphic to $\Bbb{Z}\times \Bbb{Z}$.

Trending Questions

Popular # Hahtags

Popular Questions