Question

Construct a non trivial homomorphism $\mathbb Z_{14} \to\mathbb Z_{21}$

score 883 · Answer 1 · 2026-05-02 18:33:11

883

Views

Construct a non trivial homomorphism $\mathbb Z_{14} \to\mathbb Z_{21}$

Published on 02 May 2026 - 18:33

score 40 · Answer 2 · 2026-04-17 07:54:03

40

Views

Show that if $\gamma$ is any isometry on $\mathbb{R}^n$, then so is $a\gamma(\dfrac{1}{a})$

Published on 17 Apr 2026 - 7:54

score 159 · Answer 3 · 2026-04-16 01:49:38

159

Views

show that $D_n =[e, a,a^2,...,a^n,b,ba,...,ba^{n-1}]$ forms a group

Published on 16 Apr 2026 - 1:49

score 39 · Answer 4 · 2026-04-16 23:10:34

39

Views

Can I state $f(1_{15})=48_{20}$? When $f(4_{15})=12_{20}$?

Published on 16 Apr 2026 - 23:10

score 943 · Answer 5 · 2026-04-30 06:00:07

943

Views

Conjugation in $A_n$

Published on 30 Apr 2026 - 6:00

score 62 · Answer 6 · 2026-04-16 20:33:17

62

Views

2 arguments that prove$(\mathbb{C}-\{0\},.)\not\simeq(\mathbb{R-\{0\}},.)$.

Published on 16 Apr 2026 - 20:33

score 898 · Answer 7 · 2026-04-30 14:17:26

898

Views

Symmetries of the Tetrahedron - Geometric description and isomorphic correlations

Published on 30 Apr 2026 - 14:17

score 84 · Answer 8 · 2026-04-29 12:42:41

84

Views

Subgroup generated by $S$ is $A_5$

Published on 29 Apr 2026 - 12:42

score 651 · Answer 9 · 2026-05-10 12:16:15

651

Views

Show that the group $\mathbb Z_{45}$ has exactly one subgroup of order $3$ and construct it.

Published on 10 May 2026 - 12:16

score 492 · Answer 10 · 2026-05-10 13:26:21

492

Views

All possible non-isomorphic abelian groups of order $225$ and the minimum possible collapsion

Published on 10 May 2026 - 13:26

score 30 · Answer 11 · 2026-04-17 04:37:37

30

Views

$f_1(x_{16})=9_{36},f_2(x_{16})=18_{36},f_3(x_{16})=0_{36}$ homomorphisms?

Published on 17 Apr 2026 - 4:37

score 310 · Answer 12 · 2026-05-06 05:01:55

310

Views

Show $\widehat{\mathbb{Z}}$ is isomorphic to $S^1$

Published on 06 May 2026 - 5:01

score 376 · Answer 13 · 2026-05-07 12:46:45

376

Views

Showing that $2$ of the following groups are not isomorphic

Published on 07 May 2026 - 12:46

score 41 · Answer 14 · 2026-04-14 23:40:38

41

Views

Let $G=\Bbb Z$ and $H =m\Bbb Z$. What is $(G : H)$?

Published on 14 Apr 2026 - 23:40

score 412 · Answer 15 · 2026-05-10 12:38:25

412

Views

Center $Z(G)$ of a group $G$ and applications within an exam problem

Published on 10 May 2026 - 12:38

List Question

Construct a non trivial homomorphism $\mathbb Z_{14} \to\mathbb Z_{21}$

Show that if $\gamma$ is any isometry on $\mathbb{R}^n$, then so is $a\gamma(\dfrac{1}{a})$

show that $D_n =[e, a,a^2,...,a^n,b,ba,...,ba^{n-1}]$ forms a group

Can I state $f(1_{15})=48_{20}$? When $f(4_{15})=12_{20}$?

Conjugation in $A_n$

2 arguments that prove$(\mathbb{C}-\{0\},.)\not\simeq(\mathbb{R-\{0\}},.)$.

Symmetries of the Tetrahedron - Geometric description and isomorphic correlations

Subgroup generated by $S$ is $A_5$

Show that the group $\mathbb Z_{45}$ has exactly one subgroup of order $3$ and construct it.

All possible non-isomorphic abelian groups of order $225$ and the minimum possible collapsion

$f_1(x_{16})=9_{36},f_2(x_{16})=18_{36},f_3(x_{16})=0_{36}$ homomorphisms?

Show $\widehat{\mathbb{Z}}$ is isomorphic to $S^1$

Showing that $2$ of the following groups are not isomorphic

Let $G=\Bbb Z$ and $H =m\Bbb Z$. What is $(G : H)$?

Center $Z(G)$ of a group $G$ and applications within an exam problem

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