Question

Show the klein group and <i> is not isomorphic

score 187 · Answer 1 · 2026-03-25 04:39:39

187

Views

Show the klein group and <i> is not isomorphic

Published on 25 Mar 2026 - 4:39

score 642 · Answer 2 · 2026-03-24 00:36:08

642

Views

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

Published on 24 Mar 2026 - 0:36

score 287 · Answer 3 · 2026-03-28 09:11:23

287

Views

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

Published on 28 Mar 2026 - 9:11

score 112 · Answer 4 · 2018-02-14 18:44:13

112

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 14 Feb 2018 - 18:44

score 42 · Answer 5 · 2026-03-25 06:12:17

42

Views

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

Published on 25 Mar 2026 - 6:12

score 95 · Answer 6 · 2026-03-25 09:53:56

95

Views

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

Published on 25 Mar 2026 - 9:53

score 38 · Answer 7 · 2026-03-22 08:25:15

38

Views

Finding the order of elements of a product group

Published on 22 Mar 2026 - 8:25

score 418 · Answer 8 · 2026-03-27 00:05:10

418

Views

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

Published on 27 Mar 2026 - 0:05

score 1.7k · Answer 9 · 2026-03-25 11:06:41

1.7k

Views

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

Published on 25 Mar 2026 - 11:06

score 54 · Answer 10 · 2026-03-25 09:29:55

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 190 · Answer 11 · 2018-02-26 14:53:37

190

Views

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

Published on 26 Feb 2018 - 14:53

score 249 · Answer 12 · 2018-02-26 15:07:46

249

Views

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

Published on 26 Feb 2018 - 15:07

score 375 · Answer 13 · 2026-03-25 07:48:47

375

Views

Prove 2 groups made up of rational numbers are isomorphic.

Published on 25 Mar 2026 - 7:48

score 160 · Answer 14 · 2026-03-25 07:40:47

160

Views

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

Published on 25 Mar 2026 - 7:40

score 330 · Answer 15 · 2026-03-28 04:35:45

330

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 28 Mar 2026 - 4:35

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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