Question

Proving that $D_4$ can't be expressed as an internal direct product.

score 194 · Answer 1 · 2018-09-24 04:14:57

194

Views

Proving that $D_4$ can't be expressed as an internal direct product.

Published on 24 Sep 2018 - 4:14

score 58 · Answer 2 · 2018-09-24 09:10:59

58

Views

Can someone please help me find examples of the following if they exist or not.

Published on 24 Sep 2018 - 9:10

score 227 · Answer 3 · 2026-03-25 09:39:58

227

Views

If $G= \mathbb{Z}/10\mathbb{Z}$ and $H= 2\mathbb{Z}/10\mathbb{Z}$, then the quotient group $G/H$ is isomorphic to ...

Published on 25 Mar 2026 - 9:39

score 236 · Answer 4 · 2018-09-25 12:23:56

236

Views

Additive groups $\mathbb R$ and $\mathbb C$

Published on 25 Sep 2018 - 12:23

score 79 · Answer 5 · 2026-03-25 09:33:52

79

Views

Does the notation $(G/A)/B$ actually make sense?

Published on 25 Mar 2026 - 9:33

score 166 · Answer 6 · 2026-03-25 03:22:48

166

Views

Can a field be canonically reconstructed from its multiplicative group?

Published on 25 Mar 2026 - 3:22

score 245 · Answer 7 · 2018-09-29 09:59:24

245

Views

Proof that the inverse exists in the group of units of the additive group of modulo n

Published on 29 Sep 2018 - 9:59

score 76 · Answer 8 · 2018-09-30 10:14:53

76

Views

Manipulating quotients of free groups

Published on 30 Sep 2018 - 10:14

score 653 · Answer 9 · 2026-03-25 03:24:06

653

Views

The category of Z-modules is isomorphic to the category Ab

Published on 25 Mar 2026 - 3:24

score 307 · Answer 10 · 2018-10-01 13:40:52

307

Views

Even and odd elements in more general additive groups

Published on 01 Oct 2018 - 13:40

score 91 · Answer 11 · 2018-10-01 22:39:43

91

Views

Can I find a series where an abelian series of smallest possible length is different from derived series?

Published on 01 Oct 2018 - 22:39

score 242 · Answer 12 · 2018-10-02 02:50:47

242

Views

Write $\mathbb{Z}_{20}^{\times}$ as a product of p-power cyclic groups.

Published on 02 Oct 2018 - 2:50

score 97 · Answer 13 · 2026-03-25 07:42:13

97

Views

Coprime automorphism group implies cyclic with order a cyclicity-forcing number

Published on 25 Mar 2026 - 7:42

score 1.1k · Answer 14 · 2026-03-25 11:14:49

1.1k

Views

Torsion subgroup of a finitely-generated abelian group is finite?

Published on 25 Mar 2026 - 11:14

score 340 · Answer 15 · 2018-10-08 04:47:44

340

Views

Is the order of the product of an infinite order element and finite order element always infinite?

Published on 08 Oct 2018 - 4:47

List Question

Proving that $D_4$ can't be expressed as an internal direct product.

Can someone please help me find examples of the following if they exist or not.

If $G= \mathbb{Z}/10\mathbb{Z}$ and $H= 2\mathbb{Z}/10\mathbb{Z}$, then the quotient group $G/H$ is isomorphic to ...

Additive groups $\mathbb R$ and $\mathbb C$

Does the notation $(G/A)/B$ actually make sense?

Can a field be canonically reconstructed from its multiplicative group?

Proof that the inverse exists in the group of units of the additive group of modulo n

Manipulating quotients of free groups

The category of Z-modules is isomorphic to the category Ab

Even and odd elements in more general additive groups

Can I find a series where an abelian series of smallest possible length is different from derived series?

Write $\mathbb{Z}_{20}^{\times}$ as a product of p-power cyclic groups.

Coprime automorphism group implies cyclic with order a cyclicity-forcing number

Torsion subgroup of a finitely-generated abelian group is finite?

Is the order of the product of an infinite order element and finite order element always infinite?

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