Question

$C_4\rtimes C_2$ isn't isomorphic to $C_4\times C_2$

score 68 · Answer 1 · 2026-03-30 16:46:18

68

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$C_4\rtimes C_2$ isn't isomorphic to $C_4\times C_2$

Published on 30 Mar 2026 - 16:46

score 92 · Answer 2 · 2021-10-05 16:37:06

92

Views

What defines an isomorphism of two groups?

Published on 05 Oct 2021 - 16:37

score 107 · Answer 3 · 2021-10-08 03:36:21

107

Views

Dummit and Foote Proposition 10.29 proof

Published on 08 Oct 2021 - 3:36

score 131 · Answer 4 · 2026-03-28 14:55:19

131

Views

How is $\Bbb{Z}_2\otimes \Bbb{Z}_3$ isomorphic to $\Bbb{Z}_6$?

Published on 28 Mar 2026 - 14:55

score 335 · Answer 5 · 2026-04-07 23:19:03

335

Views

Prove that we have an isomorphism from the group generated by $1/x$, $(x-1)/x$ to the symmetric group $S_3$

Published on 07 Apr 2026 - 23:19

score 1.4k · Answer 6 · 2026-04-04 07:53:19

1.4k

Views

Find a homomorphism $\phi$ from $U(30)$ to $U(30)$ such that $\ker(\phi) = \{1,11\}$ and $\phi(7) = 7$

Published on 04 Apr 2026 - 7:53

score 299 · Answer 7 · 2026-03-29 22:13:31

299

Views

Proving an Isomorphism via Generators

Published on 29 Mar 2026 - 22:13

score 92 · Answer 8 · 2021-10-12 18:25:49

92

Views

Prove that $\Bbb{Z}_2 \times \Bbb{Z}_4 \not\cong \Bbb{Z}_8$

Published on 12 Oct 2021 - 18:25

score 466 · Answer 9 · 2026-03-29 04:02:51

466

Views

If $N$ and $H$ are normal subgroups of $G$, then $N\cap H$ is also normal in $G$ and $G/(N\cap H)$ is isomorphic to a subgroup of $(G/N)\times(G/H)$?

Published on 29 Mar 2026 - 4:02

score 214 · Answer 10 · 2021-10-13 18:15:10

214

Views

Dummit & Foote 3.2.18 (and the second isomorphism theorem?)

Published on 13 Oct 2021 - 18:15

score 401 · Answer 11 · 2021-10-14 01:47:53

401

Views

Are the Rationals under addition isomorphic to any set of numbers?

Published on 14 Oct 2021 - 1:47

score 83 · Answer 12 · 2026-03-29 08:16:01

83

Views

Show $\Bbb{Z}_{30},\ \Bbb{Z}_5 \times D_3,\ \Bbb{Z}_3 \times D_5$ and $D_{15}$ are not isomorphic where $D_n$ is the dihedral group.

Published on 29 Mar 2026 - 8:16

score 45 · Answer 13 · 2026-03-30 00:22:53

45

Views

Help with proof: The group of left quotients of a right reversible, cancellative semigroup is unique up to isomorphism.

Published on 30 Mar 2026 - 0:22

score 144 · Answer 14 · 2026-04-04 07:53:20

144

Views

Showing an isomorphism on $\Bbb Z_2 \times\Bbb Z_4$

Published on 04 Apr 2026 - 7:53

score 639 · Answer 15 · 2021-10-17 19:00:47

639

Views

Two groups of same order but not isomorphic?

Published on 17 Oct 2021 - 19:00

List Question

$C_4\rtimes C_2$ isn't isomorphic to $C_4\times C_2$

What defines an isomorphism of two groups?

Dummit and Foote Proposition 10.29 proof

How is $\Bbb{Z}_2\otimes \Bbb{Z}_3$ isomorphic to $\Bbb{Z}_6$?

Prove that we have an isomorphism from the group generated by $1/x$, $(x-1)/x$ to the symmetric group $S_3$

Find a homomorphism $\phi$ from $U(30)$ to $U(30)$ such that $\ker(\phi) = \{1,11\}$ and $\phi(7) = 7$

Proving an Isomorphism via Generators

Prove that $\Bbb{Z}_2 \times \Bbb{Z}_4 \not\cong \Bbb{Z}_8$

If $N$ and $H$ are normal subgroups of $G$, then $N\cap H$ is also normal in $G$ and $G/(N\cap H)$ is isomorphic to a subgroup of $(G/N)\times(G/H)$?

Dummit & Foote 3.2.18 (and the second isomorphism theorem?)

Are the Rationals under addition isomorphic to any set of numbers?

Show $\Bbb{Z}_{30},\ \Bbb{Z}_5 \times D_3,\ \Bbb{Z}_3 \times D_5$ and $D_{15}$ are not isomorphic where $D_n$ is the dihedral group.

Help with proof: The group of left quotients of a right reversible, cancellative semigroup is unique up to isomorphism.

Showing an isomorphism on $\Bbb Z_2 \times\Bbb Z_4$

Two groups of same order but not isomorphic?

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