Question

Show the klein group and <i> is not isomorphic

score 191 · Answer 1 · 2026-05-12 23:36:42

191

Views

Show the klein group and <i> is not isomorphic

Published on 12 May 2026 - 23:36

score 648 · Answer 2 · 2026-05-12 04:58:16

648

Views

$C_m \times C_n$ isomorphic to $C_{mn}$

Published on 12 May 2026 - 4:58

score 299 · Answer 3 · 2026-05-11 22:27:57

299

Views

Isomorphy of simple groups of order 360 : a proof with a presentation

Published on 11 May 2026 - 22:27

score 115 · Answer 4 · 2026-04-15 23:20:08

115

Views

Suppose that $G$ is a commutative group, and define $f∶G → G$ by $f(a) = a^{−1}$ . Prove or disprove: $f$ is an isomorphism.

Published on 15 Apr 2026 - 23:20

score 47 · Answer 5 · 2026-05-10 15:51:57

47

Views

Define the 2-adic valuations of the integers $\Bbb{N}$ as a group

Published on 10 May 2026 - 15:51

score 99 · Answer 6 · 2026-05-13 18:03:48

99

Views

Is it possible to find-out whether given group is $\mathbb{Z}_{15}$ or else?

Published on 13 May 2026 - 18:03

score 43 · Answer 7 · 2026-04-17 04:46:24

43

Views

Finding the order of elements of a product group

Published on 17 Apr 2026 - 4:46

score 420 · Answer 8 · 2026-04-15 13:00:45

420

Views

Any field that contains the integers contains the rationals as a subfield (Analysis proof)

Published on 15 Apr 2026 - 13:00

score 1.7k · Answer 9 · 2026-05-10 12:34:25

1.7k

Views

Proof that (Z3, +) is isomorphic C3, and (Z3, +) is a proper subgroup of S3

Published on 10 May 2026 - 12:34

score 56 · Answer 10 · 2026-05-10 12:35:29

Suppose that m ∈ Z≥1, Cm is a cyclic group of order m, and φ∶ Cm → Cm is an isomorphism. Prove that if a generates Cm then φ(a) generates Cm.

score 193 · Answer 11 · 2026-04-12 22:46:51

193

Views

When are two groups isomorphic, if we have injective maps between them?

Published on 12 Apr 2026 - 22:46

score 252 · Answer 12 · 2026-04-11 01:03:52

252

Views

Difficulty in understanding isomorphism proof between 2 groups $Z_4$ and $U_5$

Published on 11 Apr 2026 - 1:03

score 378 · Answer 13 · 2026-05-10 16:13:20

378

Views

Prove 2 groups made up of rational numbers are isomorphic.

Published on 10 May 2026 - 16:13

score 163 · Answer 14 · 2026-05-10 16:10:18

163

Views

Proving that $(\mathbb{R},+) \cong (\mathbb{R}_{>1},\circ)$

Published on 10 May 2026 - 16:10

score 332 · Answer 15 · 2026-04-11 15:17:44

332

Views

Proof verification: For isomorphism $\phi : G\to H$, prove that $G$ has subgroup of order $n$ iff $H$ has subgroup of order $n$.

Published on 11 Apr 2026 - 15:17

List Question

Show the klein group and <i> is not isomorphic

$C_m \times C_n$ isomorphic to $C_{mn}$

Isomorphy of simple groups of order 360 : a proof with a presentation

Suppose that $G$ is a commutative group, and define $f∶G → G$ by $f(a) = a^{−1}$ . Prove or disprove: $f$ is an isomorphism.

Define the 2-adic valuations of the integers $\Bbb{N}$ as a group

Is it possible to find-out whether given group is $\mathbb{Z}_{15}$ or else?

Finding the order of elements of a product group

Any field that contains the integers contains the rationals as a subfield (Analysis proof)

Proof that (Z3, +) is isomorphic C3, and (Z3, +) is a proper subgroup of S3

Suppose that m ∈ Z≥1, Cm is a cyclic group of order m, and φ∶ Cm → Cm is an isomorphism. Prove that if a generates Cm then φ(a) generates Cm.

When are two groups isomorphic, if we have injective maps between them?

Difficulty in understanding isomorphism proof between 2 groups $Z_4$ and $U_5$

Prove 2 groups made up of rational numbers are isomorphic.

Proving that $(\mathbb{R},+) \cong (\mathbb{R}_{>1},\circ)$

Proof verification: For isomorphism $\phi : G\to H$, prove that $G$ has subgroup of order $n$ iff $H$ has subgroup of order $n$.

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